bib-pubdb1.desy.debib-pubdb1.desy.de/record/93879/files/thesisJRuiz.pdf · Acknowledgements I enormously thank my parents, Mr. Agustin Ru´ız y Uex and Mrs. Mar´ıa Eliz-abeth Tabasco

CENTER OF RESEARCH AND ADVANCED STUDIES

OF THE NATIONAL POLYTECHNICAL INSTITUTE

UNIT IN MERIDA

DEPARTAMENT OF APPLIED PHYSICS

K0

S production at high Q2 in

deep inelastic ep scattering at H1

A dissertation submitted by

Julia Elizabeth Ruiz Tabasco

for the degree of

Doctor in applied physics

Thesis Supervisor

Dr. Jesus Guillermo Contreras Nuno.

Merida, Yucatan, Mexico. May 2010

CENTRO DE INVESTIGACION Y DE ESTUDIOS AVANZADOS

DEL INSTITUTO POLITECNICO NACIONAL

UNIDAD MERIDA

DEPARTAMENTO DE FISICA APLICADA

Produccion de K0

S a Q2 altas en

dispersion ep inelastica profunda en H1

Tesis que presenta

Julia Elizabeth Ruiz Tabasco

para obtener el grado de

Doctora en Ciencias

en la especialidad de

Fısica Aplicada

Director de Tesis

Dr. Jesus Guillermo Contreras Nuno.

Merida, Yucatan, Mexico. Mayo de 2010

All truths are easy to understand once they are discovered;

the point is to discover them.

(Galileo Galilei)

v

Acknowledgements

I enormously thank my parents, Mr. Agustin Ruız y Uex and Mrs. Marıa Eliz-

abeth Tabasco Ruz for the education, for teach me to fight against the obstacles and

do not leave the things without finish them. By their continuous support to all my

decisions with respect to the academic and private life, and for those goodbyes and

good desires accompanied with pretty smiles even when they did not want let me go.

Thanks to my four sisters Nalleli, Adriana, Delmira and Leydi for the shared mo-

ments throughout our years together, especially to Nalle for those talks in which only

stopped laughing until the stomach hurts. Thanks to you and Delmi for give me the

opportunity of being a child again when I play with my nephews. Eternal thanks to

that house of “crazy people” in Tizimın that makes me what I am.

I also want to thank my beloved husband, the Engineer Luis R. Dzib Eliodoro for

his unconditional support, to give me the chance of professional development and to

encourage me to do the things even when everything seemed to be against. For that

optimistic way to live, for helping me to bear my frustrations and deceptions in those

long conversations drinking a beer, but mainly for undertaking with me a nice stage

of life.

Special thanks to my thesis supervisor, Dr. Jesus Guillermo Contreras Nuno for

trust my skills, for answer to my questions not only about the work but to everyone

that I did. For answering to my hundreds of emails when it was not possible to be in

the same place. For the support during the days of anger or desception, for knowing

how to deal with me in spite of my character and to offer me the opportunity to work

with him.

Eternal gratefulness to Dr. Daniel Traynor of the Queen Mary University from

London for accepting to be the supervisor of my analysis during my time at DESY,

for the explanations, comments and constant help in the accomplishment of this thesis

viii

work.

I would also like to thank the members of the H1 Collaboration for the nice time

together, especially to Drs. Hannes Hung, Albert Kutson and Dmitri Ozerov for

their help to solve my doubts with respect to the Monte Carlo programs. To Ms.

Deniz Sunar and Ms. Ana Falkiewicks, as well as to the colleagues Marc del Degan

and Maxime Gouzevitch for the discussions with respect to strangeness physics, the

technical studies necessary to carry out the analysis and the help with commands of

Root and programming in C++.

To Dr. Daniel Pitzl, Dra. Grazyna Nowak, Dra. Karin Daum, Dra. Katja

Krueger, Dr. Stefan Schmitt and Dr. Guenter Grindhammer for the interest de-

posited in this study; the continuous comments, suggestions and requests that en-

riched this analysis, but especially for the attention dedicated to my work during the

days near to the preliminary stamp of my results.

To the High Energy Physics LatinAmerican-European Network program (HELEN)

for the partial economic support during both periods of my stays at DESY. To Dr.

Fridger Schrempp, Dr. Veronica Riquer and Dr. Arnulfo Zepeda for their help with

the steps to get the Helen scholarship.

To the Consejo Nacional de Ciencia y Tecnologıa (CONACYT) for the economic

support during my doctoral studies.

To Mrs. Heidy Lucely Miranda Chable, Maricarmen Iturralde Lorıa and Guadalupe

Aguilar Martınez for the secretarial help during my studies in CINVESTAV. As well

as to Mrs. Alla Grabowsky and Sabine Platz, secretaries of DESY that offered me

their help during my stay there.

To the members of the Department of Applied Physics at CINVESTAV, for the

lessons and the nice time together in the classrooms and outside them.

To Ms. Georgina Espinoza and Mr. Mauricio Romero for their constant help

with computational equipment, that for some strange reason always stopped working

in my hands.

To the Doctors who conform the honorable synod: Dr. Jurgen Engelfried, Dr.

ix

Eduard de la Cruz Burelo, Dr. Francisco Larios Forte, Dr. Juan Jose Alvarado Gil,

and Dr. J. Guillermo Contreras Nuno.

To Ms. Angela Lucati for the beautiful friendship, the tasty apple pies and the

pleasant talks in the office. For her interest in learning Spanish and the enormous

support offered during the time living in Hamburg, but mainly for her patience and

disposition to help during my first days of stay at DESY. To Dr. Andrea Vargas for

her company in the search of Mexican ingredients in Hamburg, for the nice afternoons

cooking in her house and the nice talks that reminded me my country.

To Anastasia Grebenyuk, Tobias Toll, Lluis Marti, Federico Von Samson, Axel

Cholewa, Michal Deak, Zlatka Staykova, Krzysztof Kutak, Albert Kutson and Krzysztof

Nowak for doing the life so funny in Hamburg, for the laughters in the meetings of

’physics and cookies’ and also, why not?, for the discussions of politic, economy,

literature and physics.

And the last in the list but the first in my heart, to my dear friends of the drunk

band: Dulce Valdes, Jose Luis Albornoz, Benjamın Palma, Roberto Ramırez, Miguel

Lopez, Roberto Escalante, Marco Izozorbe, Carlos Perera and Johny Martınez, to

offer me their invaluable friendship and for acceptting me among them, but specially

for letting me be the strange girl.

Agradecimientos

Agradezco enormemente a mis padres, el Prof. Agustın Ruiz y Uex y la Sra.

Marıa Elizabeth Tabasco Ruz por la educacion brindada, por ensenarme a luchar

contra los obstaculos y no dejar las cosas sin terminar. Por el continuo apoyo ape-

sar de mis espontaneas decisiones respecto a la vida academica y privada, e incluso

por esos adioses y buenos deseos acompanados de bonitas sonrisas aun cuando en

el fondo no querıan dejarme ir. Gracias a mis cuatro hermanas Nalleli, Adriana,

Delmira y Leydi por los bonitos momentos que hemos compartido a lo largo de nue-

stros anos juntas, especialmente a Nalle por aquellas ’platicas ’ que se convertıan en

interminables risas hasta que el estomago dolıa. Gracias a tı y a Delmi por darme

la alegrıa de ser nina otra vez al jugar con mis sobrinos. Gracias eternas a esa casa

de locos en Tizimın que me convirtio en lo que ahora soy.

Quiero agradecer tambien a mi esposo el Ing. Luis R. Dzib Eliodoro por su apoyo

incondicional, por darme la oportunidad de desarrollarme profesionalmente y alen-

tarme a realizar las cosas aun cuando todo parece estar en contra. Por esa manera

optimista de vivir, por ayudarme a sobrellevar mis frustraciones y decepciones en

esas largas conversaciones bebiendo una cerveza, pero sobre todo por emprender a mi

lado una linda etapa de la vida.

Gracias especiales a mi supervisor de tesis, el Dr. Jesus Guillermo Contreras

Nuno por confiar en mi capacidad, por contestar a mis interminables preguntas no

solo del trabajo sino todas aquellas que en algun momento formule. Por responder

a mis cientos de emails cuando no era posible coincidir en el mismo lugar. Por el

apoyo durante los dias de enojo o desanimo, por saber como tratar conmigo apesar

de mi caracter y por brindarme la oportunidad de trabajar a su lado.

Un agradecimiento eterno para el Dr. Daniel Traynor de la universidad Queen

Mary de Londres por aceptar ser supervisor de mi analisis durante el tiempo que es-

xii

tuve en DESY, por sus explicaciones, comentarios y constante ayuda en la realizacion

de este trabajo de tesis.

Me gustarıa tambien agradecer a los miembros de la colaboracion H1 por la amable

convivencia, especialmente al Dr. Hannes Hung, Albert Kutson y Dmitri Ozerov

por su ayuda a resolver mis dudas respecto a los programas Monte Carlo. A la

Sritas. Deniz Sunar and Anna Falkiewicks, ası como a los colegas Marc del Degan

y Maxime Gouzevitch por las discusiones respecto a fısica de extraneza, los estudios

tecnicos necesarios para llevar a cabo el analisis y la ayuda con comandos de root y

de programacion en C++.

Al Dr. Daniel Pitzl, Dra. Grazyna Nowak, Dra. Karin Daum, Dra. Katja

Krueger, Dr. Stefan Shmitt y Dr. Guenter Grindhammer por el interes depositado

en este estudio; los continuos comentarios, sugerencias y peticiones que sirvieron

para el enriquecimiento de este analisis, pero especialmente por la atencion prestada

durante los dıas cercanos a la obtencion de estampa preliminar de mis resultados.

Al programa High Energy Physics LatinAmerican-European Network (HELEN)

por el soporte economico parcial durante los dos perıodos de estancia en DESY. Al

Dr. Fridger Schrempp, Dra. Veronica Riquer y Dr. Arnulfo Zepeda por su ayuda

con los tramites para la obtencion de la beca Helen.

Al consejo nacional de ciencia y tecnologıa (CONACYT) por el apoyo economico

durante mis anos de estudios doctorales.

A las Sras. Heidy Lucely Miranda Chable, Maricarmen Iturralde Lorıa y Guadalupe

Aguilar Martınez por la ayuda secretarial durante mi estancia en el CINVESTAV.

Ası como a las Sras. Alla Grabowsky y Sabine Platz, secretarias del DESY que me

brindaron su ayuda durante mi estancia ahı.

A los miembros del departamento de fısica aplicada del CINVESTAV, por las

ensenanzas y convivencia en las aulas y fuera de ellas.

A la Srita. Georgina Espinoza y el Sr. Mauricio Romero por la constante ayuda

con equipos de computo, que por alguna extrana razon siempre se descomponıan en

mis manos.

xiii

A los doctores que conforman el honorable sınodo, Dr. Jurgen Engelfried, Dr.

Francisco Larios Forte, Dr. Juan Jose Alvarado Gil, Dr. Eduard de la Cruz Burelo

y Dr. J. Guillermo Contreras Nuno.

A la Srita. Angela Lucati por la linda amistad, los ricos pasteles de manzana y

las agradables platicas en la oficina. Por su interes en aprender espanol y el enorme

apoyo brindado durante todo el tiempo que vivı en Hamburgo; pero principalmente

por su paciencia y disposicion de ayuda durante mis primeros dias de estancia en

DESY. A la Dr. Andrea Vargas por acompanarme en la busqueda de ingredientes

mexicanos en Hamburgo, por las agradables tardes cocinando en su casa y las platicas

populares que me hacıan recordar mi pais.

A Anastasia Grebenyuk, Tobias Toll, Lluis Marti, Federico Von Samson, Axel

Cholewa, Michal Deak, Zlatka Staykova, Krzysztof Kutak, Albert Kutson and Krzysztof

Nowak por hacer la vida divertida en Hamburgo, por las risas en las reuniones de

’physics and cookies’ y tambien, porque no?, por las discusiones de polıtica, economıa,

literatura y fısica.

Y por ultimo en la lista pero los primeros en el corazon, a mis amigos de la banda

borracha: Dulce Valdes, Jose Luis Albornoz, Benjamın Palma, Roberto Ramırez,

Miguel Lopez, Roberto Escalante, Marco Izozorbe, Carlos Perera y Johny Martınez,

por brindarme su valiosa amistad y aceptarme entre ellos, pero mas que nada por

dejarme ser la chica extrana.

Abstract

The production of K0S mesons is studied using deep-inelastic scattering events

(DIS) recorded with the H1 detector at the HERA ep collider. The measurements

are performed in the phase space defined by the four-momentum transfer squared of

the photon, 145 GeV2 < Q2. The differential production cross sections of the K0S

meson are presented as function of the kinematic variables Q2 and x, the transverse

momentum pT and the pseudorapidity η of the particle in laboratory frame, and as

function of the momentum fraction xBFp and transverse momentum pBF

T in the Breit

Frame. Moreover, the K0S production rate is compared to the production of charged

particles and to the production of DIS events in the same region of phase space. The

data are compared to theoretical predictions, based on leading order Monte Carlo

programs with matched parton showers. The Monte Carlo models are also used for

studies of the flavour contribution to the K0S production and parton density function

dependence.

xv

Resumen

La produccion de mesones K0S es estudiada usando eventos de dispersion inelastica

profunda (DIS) tomados con el detector H1 en el colisionador ep HERA. Las medi-

ciones se realizan en el espacio fase definido por el cuadrado del cuadrimomento

transferido del foton, 145 GeV2 < Q2. Las secciones trasversales diferenciales de la

produccion de K0S se presentan en funcion de las variables cinematicas Q2 y x, el

momento transverso pT y la pseudorapidez η de la partıcula en el marco del labora-

torio, y en funcion de la fraccion de momento xBFp and momento transverso pBF

T en el

marco Breit. Mas aun, la produccion de los mesones K0S se compara a la produccion

de partıculas cargadas y a la produccion de eventos DIS en la misma region de espa-

cio fase. Los resultados se comparan a predicciones teoricas basadas en programas

Monte Carlo de primer orden unidos a cascadas de partones. Los modelos Monte

Carlo tambien se usan para el estudio de la contribucion de sabor a la produccion

de K0S y la dependencia de la funcion de densidad de partones.

Preface

The understanding of the composition of matter and the way it interacts has been,

since a long time ago, the topic of investigation of several physicist whose theoretical

and experimental researches have contributed to the formulation of ideas about the

structure of the atoms. The first models indicated that the protons, neutrons and

electrons are the basic components, but further studies revealed that the proton and

neutrons are formed by other elementary pieces called quarks [1].

In 1969, ideas from Bjorken and Feynman were fundamental for the development

of a model able to explain a nucleon as a particle composed of quarks. The compo-

sition of the nucleon was described through the so called structure functions. This

model, known as the quark parton model or QPM [2] [3], expresses the structure

function F2 as the weighted sum of the momentum distribution of the quarks qi(x)

and antiquarks qi(x) in the nucleon times the square of their electric charge ei:

F2(x) =∑

i

e2i x[qi(x) + qi(x)] (1)

where x is the fraction of the proton momentum carried by the probed quark. The

quarks, in this model, carry only longitudinal momentum.

The proton (uud) is formed by two up u quarks and one down d quark, then:

∫ 1

0

(u(x) − u(x)) dx = 2

∫ 1

0

(d(x) − d(x)) dx = 1. (2)

The QPM interpretation had some success, but further studies [4] showed that

only 50% of the proton momentum is carried by the quarks, then the missing momen-

tum should be carried by another kind of partons with no electric charge. Some time

later, between 1973-78 the gluons were discovered, and quantum chromodynamics

(QCD) was proposed: the QCD age had started.

xix

xx

QCD considers that the quarks carry not only electric charge but also colour

charge. The exchange of colour is mediated by the gluons with spin 1. Due to

the new assumption, QCD also should consider the possibility that quarks radiate

gluons, and the possibility of gluon fluctuations into quarks which is the source of

the sea of quarks inside the proton. These processes complicate the calculations of

proton structure function F2 but good experimental results have been obtained as

shown in Figure 1 where F2 is plotted versus the four-momentum squared of the

transfer photon in the DIS events, Q2. The F2 data for x values around 0.25 is flat

as a function of Q2, this is called Bjorken scaling. For smaller values of x, F2 grows

logarithmically with Q2, this is called scaling violation.

QCD together with the electroweak theory form the so called Standard Model

(SM) which is a very successful theory of elementary particles, in spite of its known

shortcomings.

The SM includes 61 elementary particles, 48 of them of spin 1/2 (or fermions):

36 quarks (the quarks up, down, charm, strange, top and bottom, presented in three

different colors; and their antiparticles) and 12 leptons (the electron, muon, tau, their

neutrinos, and their respective antiparticles) which are classified according to their

way of interaction. The SM explains the forces as resulting from matter particles

exchanging other particles, the mediating particles (12 elementary particles) with

spin 1 (bosons): the photon γ for the very well known electromagnetic force, the W±

and Z0 boson for the weak interactions and the gluon g (8 different gluons) for the

strong interaction. Figure 2 shows the Standard Model of the elementary particles.

The Higgs boson (also considered as elementary particles) is still an hypothetical

particle, that would explain the fundamental mass of the particles.

Hadrons, strongly interacting particles, are classified as mesons or baryons if they

are made of a quark-antiquark pair (qq) or of three quarks (qqq), respectively. The

proton is an stable baryon as far as we know. The nucleon, another baryon, is

relatively stable only when bound in a nuclei. All other hadrons decay very fast, in

a human time scale, so they are not found in ordinary matter. This characteristic is

xxi

10-3

10-2

10-1

1

10

10 2

10 3

10 4

10 5

10 6

1 10 102

103

104

105

Q2 / GeV2

F 2 ⋅

2i

x = 0.65, i = 0

x = 0.40, i = 1

x = 0.25, i = 2

x = 0.18, i = 3

x = 0.13, i = 4

x = 0.080, i = 5

x = 0.050, i = 6

x = 0.032, i = 7

x = 0.020, i = 8

x = 0.013, i = 9

x = 0.0080, i = 10

x = 0.0050, i = 11

x = 0.0032, i = 12

x = 0.0020, i = 13

x = 0.0013, i = 14

x = 0.00080, i = 15

x = 0.00050, i = 16

x = 0.00032, i = 17

x = 0.00020, i = 18

x = 0.00013, i = 19

x = 0.000080, i = 20x = 0.000050, i = 21 H1 e+p

ZEUS e+p

BCDMS

NMC

H1 PDF 2000

extrapolation

H1

Col

labo

ratio

n

Figure 1: Experimental results of the F2 structure function of the proton as functionof the four-momentum squared of the transfer photon Q2 and the proton momentumfraction carried by the struck quark x, compared to NLO calculations in QCD (solidline shows the H1 PDF 2000 [5]). At low Q2, the H1 data are complemented withthe fixed target experiments BCDMS[6] and NMC[7], [8] data.

xxii

Figure 2: Standard model constituents.

one of the issues that makes important their study in particle physics.

This thesis is focused in the research of a meson known as the K0S which belongs

to the family of strange mesons due to the presence of a strange s quark in its

composition.

The first observed mesons were the pion π and the kaon K, in 1947 [9] using a

cloud chamber. The kaon decay was observed by G.D. Rochester and C.C. Butler,

then other mesons were observed in several experiments. The lifetimes differences

of the kaons and the observation of pair production of strange particles from strong

interaction of non-strange hadrons, as that one shown in Figure 3, suggested that

they contain a new quark, the strange quark s, having the same electric charge as

the d quark but higher mass because K and Σ are heavier than π+ and p. Then

a new quantum number, called strangeness, was introduced by M. Gell-Mann and

A. Pais [10]. The strangeness quantum number is conserved in strong, but violated

in weak interactions.

The discovery of hadrons with strangeness quantum number marked the begin-

ning of an exciting age in particle physics which, after more than 60 years, have not

found its conclusion yet. However the studies continue, as the one carried out for

this doctoral thesis whose main goal is the analysis of the lightest strange meson,

xxiii

__

+

p

K+

+

Figure 3: The production of strange particles in the interaction of non-strangehadrons π+ + p → K+ + Σ+.

the K0S, decaying mainly into two pions with opposite electric charges.

The goal of this thesis is to contribute to the strangeness studies throught the

determination of the total and differential cross sections of the K0S meson production

at high Q2 range using HERA II data from 2004 to 2007, since they provide plenty of

statistics making possible the study at this range which was not been possible in the

previous years of HERA operation, and provide valuable information of fundamental

aspects in QCD dynamics, understanding of K0S production, comparison of parton

density functions and strangeness factor values for MC tests.

The thesis is structured as follows. In the first chapter the deep inelastic scattering

and its kinematics are introduced, the main aspects of the theoretical framework in

which the Monte Carlo simulation programs are based can also be found there.

The second chapter consists on the presentation of the K0S meson, the production

mechanisms and the importance of the strangeness studies. Previous results of differ-

ent experiments corresponding to the strange topic are briefly summarized, the most

recent measurements of strange particles by the H1 collaboration are emphasized as

the main introduction to the work presented here.

The third chapter is dedicated to the description of the HERA collider and the

H1 detector components as well as to the explanation of the performance of trackers

and calorimeter detection devices, trigger system and luminosity measurement.

xxiv

The fourth chapter concentrates on the selection criteria of deep inelastic scatter-

ing events. The K0S reconstruction through the identification of its track daughters

and the signal extraction from its invariant mass distribution can also be found in

this chapter. The selection criteria to obtain the charged particle sample needed for

cross section ratios are explained in the last subsection.

Chapter five introduces the procedure to determine the total and differential cross

sections. The main corrections needed in the measurements and the statistical and

systematic uncertainties sources are explained in detail.

The last chapter, number six, is reserved to the results of the K0S production,

differential cross sections in the laboratory and Breit frames, production ratios of

the K0S to charged particle and DIS events, double differential cross section, as well

as complementary studies such as the PDFs dependence and flavour contribution to

the K0S production are shown. The last section presents the conclusions.

Contents

Abstract xv

Resumen xvii

Preface xix

1 Theoretical framework 1

1.1 Deep inelastic scattering . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Theoretical DIS cross section . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Event generators: Monte Carlo programs . . . . . . . . . . . . . . . . 4

1.3.1 Colour dipole model and parton showers . . . . . . . . . . . . 6

1.3.2 Fragmentation and hadronization . . . . . . . . . . . . . . . . 7

1.4 Django and Rapgap Monte Carlo programs . . . . . . . . . . . . . . . 10

1.4.1 Django . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4.2 Rapgap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Strange mesons 13

2.1 What is a K0S meson? . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Production of K0S . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Why strangeness studies are important? . . . . . . . . . . . . . . . . 19

2.4 Previous strangeness production studies . . . . . . . . . . . . . . . . 22

2.4.1 At e+e− colliders . . . . . . . . . . . . . . . . . . . . . . . . . 22

xxv

xxvi CONTENTS

2.4.2 At pp and heavy ions collisions . . . . . . . . . . . . . . . . . 23

2.4.3 At ep colliders . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5 Previous H1 results of strangeness at low Q2 . . . . . . . . . . . . . . 27

2.5.1 Search of resonances . . . . . . . . . . . . . . . . . . . . . . . 27

2.5.2 Analysis of K∗(892) meson production . . . . . . . . . . . . . 30

2.5.3 K0S and Λ studies at low Q2 . . . . . . . . . . . . . . . . . . . 32

3 HERA and the H1 Detector 39

3.1 The HERA collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2 The H1 detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2.1 Tracker system . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2.1.1 Central silicon tracker . . . . . . . . . . . . . . . . . 50

3.2.1.2 Central jet chambers . . . . . . . . . . . . . . . . . . 50

3.2.1.3 Central z chambers . . . . . . . . . . . . . . . . . . . 51

3.2.1.4 Central proportional chambers . . . . . . . . . . . . 52

3.2.2 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2.2.1 Liquid argon calorimeter . . . . . . . . . . . . . . . 53

3.2.2.2 Spaghetti calorimeter (SPACAL) . . . . . . . . . . . 55

3.2.3 Luminosity system . . . . . . . . . . . . . . . . . . . . . . . . 56

3.2.4 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4 Selection of DIS events and K0S candidates 59

4.1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2 Data quality constrains . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2.1 Run sample selection . . . . . . . . . . . . . . . . . . . . . . . 61

4.2.2 Vertex cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2.3 DIS kinematic range . . . . . . . . . . . . . . . . . . . . . . . 63

4.3 Selection of DIS events . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.3.1 Scattered electron energy . . . . . . . . . . . . . . . . . . . . . 64

4.3.2 Scattered electron polar angle and zimpact coordinate . . . . . 64

CONTENTS xxvii

4.3.3 Four-momentum conservation . . . . . . . . . . . . . . . . . . 65

4.4 Reconstruction of K0S candidates . . . . . . . . . . . . . . . . . . . . 65

4.4.1 Track cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.4.2 Cuts to the K0S candidates . . . . . . . . . . . . . . . . . . . . 67

4.5 Event yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.6 Signal extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.7 Selection of charged particles . . . . . . . . . . . . . . . . . . . . . . . 76

5 The measurement of the cross section 77

5.1 Determination of the cross section . . . . . . . . . . . . . . . . . . . . 77

5.1.1 Binning scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.2 The correction of data . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.2.1 Control plots . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.2.2 Reweighting procedure . . . . . . . . . . . . . . . . . . . . . . 87

5.2.3 Purity and Stability . . . . . . . . . . . . . . . . . . . . . . . 88

5.2.4 Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.2.5 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.3 The systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . 95

5.3.1 Energy and polar angle of the electron . . . . . . . . . . . . . 98

5.3.2 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.3.3 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.3.4 Model dependence . . . . . . . . . . . . . . . . . . . . . . . . 101

5.3.5 Track efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.3.6 Trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.3.7 Signal extraction . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.3.8 Branching ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6 Results and conclusions 107

6.1 Total K0s cross section . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.2 Differential K0s cross section . . . . . . . . . . . . . . . . . . . . . . . 109

xxviii CONTENTS

6.3 Ratios of the differential cross sections . . . . . . . . . . . . . . . . . 110

6.3.1 Differential K0S/h± cross section . . . . . . . . . . . . . . . . . 115

6.3.2 Differential K0s /DIS cross section . . . . . . . . . . . . . . . . 115

6.4 Double differential cross section . . . . . . . . . . . . . . . . . . . . . 119

6.5 Comparison to QCD models . . . . . . . . . . . . . . . . . . . . . . . 119

6.5.1 Parton distribution functions . . . . . . . . . . . . . . . . . . 120

6.5.2 Flavour contribution . . . . . . . . . . . . . . . . . . . . . . . 121

6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

A Reconstruction methods 129

A.1 The electron method . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

A.2 The hadron method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

A.3 The double angle method . . . . . . . . . . . . . . . . . . . . . . . . 130

A.4 The sigma method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

A.5 The electron-sigma method . . . . . . . . . . . . . . . . . . . . . . . 131

B Multiwire proportional and drift chambers 133

C Q and t measurement 137

D Track reconstruction 141

E Breit frame of reference 145

F Fits to mass distributions 149

G Resumen del trabajo de tesis 167

Bibliography 173

Chapter 1

Theoretical framework

The ep HERA collider at DESY enables through deep inelastic scattering (DIS)

events the study of the proton composition and the test of the Standard Model

and other aspects of Quantum Chromo Dynamics. The kinematic variables for the

description of the events are presented in this chapter, as well as the theoretical

framework of the simulation programs for DIS processes. The Lund fragmentation

model of hadronization describing the mechanism of hadron creation, an essential

part of the Monte Carlo programs, is presented.

1.1 Deep inelastic scattering

In 1911, Rutherford unexpectedly discovered the subatomic structure using the

scattering technique. An analogue of such a technique is used today in high energy

particle physics to study the substructure of hadrons. For DIS at HERA, the hadron

is a proton studied by the scattering of an electron beam off it.

The Deep Inelastic Scattering process at HERA consists in the interaction

of incoming electrons1 with incoming protons through the exchange of a virtual

boson [4]. The proton breaks up resulting in a final hadronic state system.

1For simplicit, the incoming and scattered electrons are always referred as ’electrons’, althoughthe data studied here were obtained with both electorns and positron beams.

1

2 CHAPTER 1. THEORETICAL FRAMEWORK

The DIS process can be of two types depending on the kind of the exchanged

boson. The neutral current process (NC-DIS), ep → eX, consists in the exchange of

a neutral gauge boson, a photon γ or a Z0 boson, X represents the hadronic final

states. The charged current process (CC-DIS), ep → νeX, is mediated by a charged

gauge boson W±, at the end there are a hadronic state system and a neutrino of the

electron.

Figure 1.1 shows the diagram of a NC-DIS event, the incoming electron e with

four-momentum k interacts with a quark of the incoming proton p which carries a

xP fraction of the four-momentum P of the proton, through the interchange of a

neutral virtual gauge boson (γ or Z0) with four-momentum q. After the interaction,

the scattered electron e′ has final four-momentum k′ and the proton breaks up into

a multiparticle state of hadrons denoted as X. The contribution of the Z0 boson to

the process only becomes significant at very high Q2 values compared to its mass2

squared. The CC-DIS events are not considered in this analysis.

a)

p

P=(Ep,p→

p)

X

qs (xP)q

γ, Z0 (q)

e+

k=(Ee,p→

e)

e+

(k’)

Figure 1.1: Neutral Current Deep Inelastic Scattering diagram, the four-momentumof the incoming electron (k), the scattered electron (k′) and the incoming proton (P )are shown. The transfer gauge boson can be γ or Z0.

The Q2 variable provides the specific wavelength λ = h/√

Q2 that allows to quan-

tify the resolution power of the experiment for the study of the proton components:

2MZ0 = 91.1876 ± 0.0021 GeV [11].

1.1. DEEP INELASTIC SCATTERING 3

if it increases then the resolution also increases.

1.1.1 Kinematics

The kinematics of the DIS process, for a fixed center of mass energy√

s, can be

described by two independent variables commonly chosen from the Lorentz invari-

ant variables: the negative squared of the four-momentum of the virtual exchanged

boson −q2 = Q2, the invariant mass squared of the final hadronic system W 2, the

dimensionless Bjorken scaling variable x and the inelasticity y. x represents the frac-

tion of the proton momentum carried by the struck quark and y corresponds to the

fractional energy transferred from the electron to the hadronic system in the proton

rest frame. The variables can be determined by the expressions: take values in

s = (k + P )2 (1.1)

Q2 = −q2 = −(k − k′)2 (1.2)

W 2 = (p + P )2 (1.3)

x =Q2

2P · q (1.4)

y =P · qP · k (1.5)

Neglecting the mass of the proton, the following relations are satisfied:

s ≈ 4EeEP (1.6)

Q2 ≈ sxy (1.7)

W 2 ≈ Q2

(

1 − x

x

)

(1.8)

where Ee and EP are the energies of the incoming electron and proton, respectively.

The correct reconstruction of DIS kinematics depends on how well the detector mea-

sures the neccessary variables for the calculation. Typically, the variables used for

reconstruction are the energy of the incoming and scattered electron Ee, E ′

e, the

polar angle Θe of the scattered electron, the sum Σ = Eh − pz,h of each hadronic


final particle h and the inclusive angle γ of the hadronic system. There are three

basic methods sensitive to kinematic reconstruction [12]: those based on electron

information only (e electron method), those based on hadronic final measurements

only (Σ sigma method) and those combining electron and hadronic information (DA

double angle method). To know more about the different methods of reconstruction

see appendix A. The method chosen for this analysis is the electron method.

1.2 Theoretical DIS cross section

In the lowest-order perturbation theory for QCD, the DIS cross section can be

expressed in terms of the product of leptonic and hadronic tensors associated with

the coupling of the exchanged bosons at the upper and lower vertices:

d2σ

dxdy=

2πyα2

Q4

∑

j

ηjLµνj W j

µν .

where the summation is over j = γ, Z for NC-DIS, ηj denotes the corresponding

propagators and couplings, Lµνj is the lepton tensor associated with the coupling

of the exchange boson to the leptons and the hadronic tensor W jµν describes the

interaction of the appropiate electroweak currents with the proton.

The part of the lepton tensor is very well understood but the proton structure

functions defined in terms of the hadronic tensor are not. The best attempt of the

complete modeling of DIS event is made by the Monte Carlo simulation programs.

1.3 Event generators: Monte Carlo programs

The Monte Carlo programs (MC) are computational tools for simulation in the

physical and mathematical sciences, business, economy, telecommunications, design,

and even games. They are very useful and successful methods due to their ability for

modeling systems with a large number of degrees of freedom, many-body problems

and/or systems under complicated conditions.

1.3. EVENT GENERATORS: MONTE CARLO PROGRAMS 5

The applications to high energy physics are related to the design of detectors, ac-

celerators and detectors performance, difficult QCD calculations by the evaluation of

difficult integrals and sample random variables governed by complicated probability

density functions.

In MC programs for DIS particle physics, the hadronic tensor part of the cross

section is considered as a convolution of matrix elements ME, parton density func-

tions PDFs and fragmentation functions Dfrag. The separation of matrix elements

(the interaction of the parton with the boson) and PDFs (the partonic structure of

the proton) is given by the factorization scale µF as shown in Figure 1.2. The mean-

ing of µF can be understood roughtly as: if the emission with transverse momenta is

below µF they are accounted within the PDF, if it is higher than µF are included in

the interaction. In inclusive DIS, the default choice for the scales is usually µF = Q2.

K0s

K0s

K*+

F

Figure 1.2: The factorization scheme of a DIS event showing the perturbative crosssection eγ∗, the non-perturbative parton density function (PDF).

PDFs are non-perturbative objects which can not be computed within pQCD,

but the evolution of PDFs as they move in phase space can be computed perturba-

tively. Several groups have proposed fits for the PDFs based on different theoretical


assumptions, the two most famous approaches are the DGLAP [13] (Dokshitzer, Gri-

bov, Liatov, Altarelli, Parisi) and the BFKL [14] (Balitsky, Fadin, Kuraev, Lipatov)

evolution equations.

The MC event generators involve several stages, the generation of an event starts

with the random generation of the kinematics and partonic channels of whatever

hard scattering process (the ME) the user has requested. This is then followed by the

parton cascade (CDM and MEPS as chosen in the MCs simulated for this analysis,

see section 1.3.1) down to a scale ∼ 1 GeV that separates the perturbative and non-

perturbative part of the simulation. These cascades are governed by a model of the

evolution equations previously mentioned. Once the partonic configuration has been

generated, the fragmentation process (where the parton fragmentation functions take

place) starts to model the hadronization of the final state system. The Lund string

model has been chosen for the MCs used in this analysis, the description can be

found in the subsection 1.3.2.

1.3.1 Colour dipole model and parton showers

As mention above, two different parton cascade approaches are applied for the

two DIS MCs used in this thesis: the colour dipole mode (CDM) and the parton

showers (MEPS).

The CDM model describes the parton radiation in terms of a colour field gener-

ated by a chain of radiating colour dipoles extending between a pair of colour charges.

A gluon is emitted from a colour dipole forming two independent colour dipoles as

shown in Figure 1.3 a). Further gluons can be radiated, leading to a chain of colour

dipoles, where one gluon connects two dipoles, and one dipole connects two gluons.

The CDM evolving parton cascade has no strong ordering in the transverse momenta

kT of the emitted gluons.

On the other hand, the MEPS model considers that a parton of the proton can

initiate a parton shower by radiating gluons, which become increasingly space-like

(m2 < 0) after each branching, see Figure 1.3 b). After the exchanged electroweak


K0s

K0s

K*+

K0s

K0s

K*+

Figure 1.3: The Django and Rapgap MCs scheme used in this thesis. It is possibleto observe the MC treatment of the DIS events: the matrix elements, marked σ,the parton density funcion PDF and the parton cascade simulated according to a)the colour dipole model and b) the parton shower, and the hadronization processmodeled with the string fragmentation model.

a) b)

boson is absorbed, the struck quark becomes on-shell (has a time-like virtuality

m2 > 0). In the latter case a final state shower will result, with both the virtuality

of the struck quark and the off-shell mass of the radiated gluon decreasing after each

successive branching. Any time-like parton produced in an initial shower will have

a similar evolution.

The parton shower is based on DGLAP equations with strong ordering in the

transverse momenta kT of the emitted gluons.

1.3.2 Fragmentation and hadronization

The hadronization process is a long-distance transition from the free coloured

quarks at parton level to the colour neutral final states or hadrons, involving only

small momentum transfers. The idea is based on the independent splitting or frag-

mentation of each parton, gluon or quark from the parton cascade or the hard process,

which then mix (hadronize) to create the final baryons and mesons.


The fragmentation process evolves perturbatively, so the fragmentation functions

can be determined describing the production of hadrons h from a quark q at a given x-

Bjorken value and four-momentum transfer squared Q2. However, the hadronization

mechanism can not be treated perturbatively so detailed phenomenological predic-

tions have been developed. The two commonly used models are the cluster fragmen-

tation and the string fragmentation, both are expected to be universal which means

that should reproduce results from e+e− collisions and ep scattering. For the MCs

generated for this analysis only the string fragmentation model is used, since have

been found that the cluster model does not describe the DIS physics.

q_ q

_

q_

q_

q_

q_

q_

q_

q_

q_

q_

Dis

tanc

e

q

q

qq

q

q

q

q

q

q

q

Time

Mesons

Figure 1.4: The string fragmentation model.

The scheme of hadronization by the Lund string fragmentation model [15] con-

siders the colour field between the partons, quarks and gluons, to be the fragmenting

entity rather than the partons themselves. In it, a produced quark-antiquark can be

viewed as moving apart from their common production vertex in opposite directions,

losing kinetic energy to the colour field, represented by a colour string stretching

between them and providing a linear rise of the potential energy stored in the colour

string due to their separation. When the potential becomes energetically favourable,

the string breaks up into two new qq colour strings forming out of the vacuum (or


colour field). If the invariant mass of either of these two resulting colour strings

is large enough, the breaking continues iteratively, creating more qq pairs, see Fig-

ure 1.4. The gluons are supposed to produce kinks on the string, each initially

carrying localized energy and momentum equal to that of its parent gluon.

In this model, the string break up process proceeds until only on mass-shell

string fragments combined into mesons and baryons remain. The qq pairs are

created according to the probability of a quantum mechanical tunneling process.

The production probability can be estimated from the product of the q and the q

wave functions and the colour field potential [16]. Due to the dependence on the

parton mass and/or the hadron mass, the production of strange and, in particu-

lar, the heavy quark hadrons is suppresed. The relative production is assumed as

u : d : s : c ≈ 1 : 1 : 0.3 : 10−11. The charm and heavier quarks (b and t) are not

expected to be produced in the soft fragmentation, but only in perturbative cascade

branchings g → qq.

The model considers as important free parameters for the production of strange

particles the following relative production probabilities:

• The strangeness suppression factor λs = P (s)/P (q), expresing the ratio pro-

duction probability of strange quark s to light quarks up u and down d.

• The diquark suppression factor λqq = P (qq)/P (q), which gives the production

probability of a light diquark pair P (qq) relative to a light single quark pair

P (q).

• The strange diquark suppression factor λsq = (P (sq)/P (qq))/(P (s)/P (q)) pro-

viding the ratio probability of a diquark pair production containing a strange

quark P (sq) to the diquark pair production P (qq), normalised to the strangeness

suppression factor.

Although in detail, the string motion and fragmentation is more complicated

with the appearance of additional string regions during the time evolution of the


system, the scheme is infrared safe. After the particles have been produced with

the hadronization model, the MC programs use the measured decay channels and

branching ratios to simulate their decays, yielding at the end of the process a list of

stable particles.

1.4 Django and Rapgap Monte Carlo programs

In this analysis, two Monte Carlo generators are considered: Django and Rapgap.

Both MCs simulate lepton-nucleon scattering physics, the difference radicates in the

treatment of the parton cascade process: Django is based on CDM and Rapgap

in MEPS. The hadronization process is chosen to be the Lund string fragmentation

model [15] as implemented in the JETSET program [17], tuned to ALEPH parameter

values [18]: λs = 0.286, λqq = 0.108 and λsq = 0.690.

Two sets of MCs are generated for each Django and Rapgap, one including the

possibility of the initial and final radiation which is called the radiative MC and one

without including this possibility, the so called non-radiative MC.

The radiative events are passed through the GEANT [19] simulation of the H1

apparatus in order to reproduce the detector response (reconstructed MC) whereas

the non-radiative MC are produced only at the parton level. Both are used for data

corrections.

The MC’s for comparison to data are generated without including initial and

final radiation with CTEQ PDF for the three different strangeness values λs =0.22,

λs =0.286 and λs =0.3. And other MC samples are produced with λs =0.286 but

considering as PDFs the CTEQ6L, H12000LO and GRV98.

1.4.1 Django

The Django [20] simulator of ep scattering events assigns the event proper-

ties, as the phase space, the initial conditions and the kinematic cuts with HER-

ACLES [21] [22]. The QCD part is implemented by LEPTO [23] or ARIADNE [24].

1.4. DJANGO AND RAPGAP MONTE CARLO PROGRAMS 11

Django as used for this work uses ARIADNE to generate the cascade of partons and

is based on the colour dipole model CDM.

Different PDFs can be used with the MCs. For this MC, the used PDFs are

CTEQ6LO [25], GRV98 [26], and H12000LO [5]. The renormalisation and factoriza-

tion scale are placed to µR = µF = Q2.

In total, there are four simulated radiative samples of events with Django, each

corresponding to the data periods where HERA ran either with electrons or positrons.

From the Django samples, one corresponds to the 2004e+p period, has 7 millons

of events and luminosity value equals to 1535 pb−1; for 0405e−p year there are 14

million events with corresponding luminosity of 3048 pb−1; for 2006e−p the MC has

7 millions of events corresponding to a luminosity value of 1524 pb−1 and the sample

for 0607e+p with 20 millions of events and 4383 pb−1 of luminosity.

The non-radiative files for each year period correspond to samples of 20 mil-

lion of events with luminosity of approx. 6320 pb−1 for the samples with e−p and

approximately 6379 pb−1 for the samples with e+p.

1.4.2 Rapgap

In Rapgap MC [27] the DIS events are simulated by LEPTO. The hard interaction

is taken as the standard model electroweak cross section and the implementation of

QCD parton showers at leading order are based on DGLAP splitting functions in

leading order αs. The matrix elements for leading order αs processes, as BGF and

QCDc, and the QED corrections are included by the interface to HERACLES event

generator.

The same PDFs (CTEQ6LO, GRV98 and H12000LO), normalisation and factor-

ization scales (µR = µF = Q2) as in Django, were used for Rapgap in order to be

congruent in the comparison between both models.

The radiative samples for Rapgap are of 6 millons of events for 2004e+p with

luminosity of 1529 pb−1; for 0405e−p are 12 millions of events with luminosity of

3034 pb−1; the 6 millions of events for the 2006e−p period has luminosity equals


to 1516 pb−1 and for 0607e+p period are 12 millions of events and luminosity of

3056 pb−1.

The non-radiative samples consist of 20 millions of events for each year with

L = 6920 pb−1 for the periods with e−p collisions and L = 6996 pb−1 for those with

e+p.

Chapter 2

Strange mesons

There are several interesting topics in particle physics which are not completely

understood yet. The study of K0S meson production in DIS improves the cur-

rent understanding of the particle creation during hadronization, the mechanism

of strangeness production, QCD aspects related to strange quarks, and allows to

study the resonant production of particles including K0S in their decay modes, like

heavier standard particles or exotic particles like glueballs.

In this chapter, the most relevant properties of the K0S particles, their different

production mechanisms and previous related results obtained in e+e−, heavy ion and

ep collisions are presented. Special emphasis is given to most recent results of the

H1 collaboration K0S production at low Q2 values.

2.1 What is a K0S meson?

As mentioned in the preface, nature is made of strongly interacting particles

called hadrons. There are two kind of hadrons, baryons and mesons. The baryons

are bound states of three quarks, while mesons are bound states of a quark and an

antiquark.

Mesons have also angular momentum J = L+S, where L represents the orbital

angular momentum (L = 0,1,2,...) and the meson spin is denoted by S (S = 0,1).

13

14 CHAPTER 2. STRANGE MESONS

When the meson has L = 0, it is called pseudoscalar or vector depending whether

S = 0 or S = 1, respectively.

If only the three lighter quarks (up u, down d and strange s) of the standard

model are taken into account, something known as SU(3) algebra, there are eight

pseudoscalar and eight vector mesons. Using their properties – the strangeness quan-

tum number S, charge Q, isospin I3 or mass – it is possible to plot the particles in

a coordinate system and obtain geometric figures of remarkable shape, as the octect

of pseudoscalar mesons [11] shown in the Figure 2.1 and listed in Table 2.1.

Figure 2.1: Octect of the pseudoscalar mesons plotted in the axis corresponding tostrangeness quantum number S, charge Q and isospin I3.

An important observation is that K0 can be produced by non-strange particles

together with a hyperon [28], but K0 is only produced in association with a Kaon or

a hyperon:

π+ + p → Λ + K0

S 0 0 − 1 + 1

π+ + p → K+ + K0 + p

S 0 0 + 1 − 1 0

this indicates that K0 and K0 have different strangeness quantum number. Then,

the question is how to establish the presence of these two mesons.

2.1. WHAT IS A K0S MESON? 15

Table 2.1: List of the pseudoscalar and vector mesons with the specification of theirquark content.

Pseudoscalar Vector

Particle symbol Quark content Particle symbol Quark content

π− ud ρ− ud

π0 1/√

2(dd − uu) ρ0 1/√

2(uu − dd)

π+ ud ρ+ ud

K0 ds K∗0 ds

K+ us K∗+ us

K− us K∗− us

K0 ds K∗0 ds

η′ ss φ ss

Although both are usually produced via the strong force, they decay weakly. As

weak interactions do not conserve strangeness, once they are created one can turn

into another. The K0 can turn into a K0 and then turning back to the original K0,

and so on. The Figure 2.2 shows a strange quark in the K0 turning into a down quark

by successively emitting two W-bosons of opposite charge. The down antiquark in

the K0 turns into a strange antiquark by absorbing them.

_

__ _

Figure 2.2: Diagram of the K0 turning into a K0. A strange (down) quark (anti-quark) from the K0 turns into a down (strange) quark (antiquark) by the emissionof two W -bosons of opposite charge.

Experimentally it was found that a K0 produced by strong interactions decays


with two different lifetimes [28]: K0 → ππ and K0 → πππ, so K0 seems to be two

different particles when studying its weak decays. The same is observed for K0.

This implies that if one has a pure K0 state at t = 0, at any later time t one will

have a superposition of both K0 and K0 (equation 2.1). It is known that particles

decaying by weak interactions are eigenstates of charged parity (CP), expressed as

the equation 2.2.

|K(t) > = α(t) |K0 > + β(t) |K0 >, (2.1)

CP |K0 > = |K0 > . (2.2)

Since K0 and K0 are not CP eigenstates, there must be linear combinations:

|K0S > =

1√2

(

|K0 > + |K0 >)

CP = +1, (2.3)

|K0L > =

1√2

(

|K0 > − |K0 >)

CP = −1. (2.4)

These two different modes of decay were observed by Leon Lederman and his

coworkers in 1956, establishing the existence of the two weak eigenstates called K0S

as referred in equation 2.3 and K0L as referred in equation 2.4. Later, James Cronin

and Val Fitch in 1964 (Nobel Prize in 1980) showed that a small CP symmetry

violation exists, but the states already assumed are still a very good approximation.

Since the mass of K0L is just a little larger than the sum of the masses of three

pions, this decay proceeds very slowly, about 600 times slower than the decay of K0S

into two pions.

The main properties of the K0S are I(JP ) = 1

2(0−), the mass value of 497.648 ± 0.022

MeV and the lifetime value τ = 0.8953 x 10−10 ± 0.0005 s or cτ = 2.6786 cm [11].

The K0S mesons decay by three different general modes: hadronic, with photons or

lepton anti-lepton ll, and semileptonic. The hadronic modes containing the most

frequent decay channels are listed in Table 2.2.

2.2. PRODUCTION OF K0S 17

Table 2.2: The K0S most frequent hadronic decay channels and their branching ratio

values [11].

K0S Decay channel Branching ratio

π0π0 30.69 ± 0.05 (%)

π+π− 69.20 ± 0.05 (%)

π+π−π0 3.5+1.1−0.9 x 10−7

2.2 Production of K0S

The strange quark s is not so heavy as the bottom (mb = 4.2 +0.17−0.07 GeV), charm

(mc = 1.27 0.07−0.11 GeV) or top quarks (mt = 171.2 ± 1.1 ± 1.2 GeV) but it is also not

light as up (mu = 2.55 +0.75−1.05 MeV) or down (md = 5.04 +0.96

−1.54 MeV) quarks. It has a

mass value of 105+25−35 MeV [11] what allows its creation in ep collisions at HERA.

There are different mechanisms of strange particle production, which are illus-

trated schematically in Figure 2.3, the hard interaction or QPM process, the boson

gluon fusion process (BGF), heavy decays and hadronization processes.

The hard interaction or QPM process occurs when the photon of the DIS

event interacts directly with a s quark belonging to the quarks of the proton sea.

This process involves a large momentum transfer, Figure 2.3 a).

The strange production through BFG process consists of the photon inter-

acting with a gluon emitted by the proton, which splits into a ss quark pair, see

Figure 2.3 b). As the gluon density of the proton increases at small Bjorken scaling

variable x, the BFG becomes more important at low x values.

The Figure 2.3 c) shows the heavy decay process . It is similar to the BFG

process but in this case the gluon splits into heavy quarks (c and b); then they decay

into s quarks. Due to the small probability to find c and b quarks in the proton sea,

this is the main mechanism of strangeness production by heavy quarks. At low Q2

values this process is highly suppressed due to the masses of the heavy quarks, but


−

−

−

*

−

−

−

−

Figure 2.3: The four different mechanisms of strange particle production: a) hardinteraction or QPM process, b) boson gluon fusion (BGF), c) heavy quarks decaysand d) hadronization.

a) b)

c) d)

2.3. WHY STRANGENESS STUDIES ARE IMPORTANT? 19

at very high Q2 where the quark masses are not relevant with respect to the process

scales, this process can contribute significantly.

The hadronization process is due to the colour field fragmentation as showed

in Figure 2.3 d). This is the only process which can not be treated perturbatively,

so phenomenological models are needed for its description, such as the LUND string

model. Furthermore, this process provides the largest contribution of strangeness

production over most of the phase space.

2.3 Why strangeness studies are important?

The study of strangeness has been done since the discovery of the first two mesons,

the pion and the kaon, in cosmic rays in 1947 which marked the birth of this subject

on particle physics.

It is interesting because the strange flavour does not exist in ordinary matter, it

appears at colliding machines when the center of mass energy of the reaction is much

larger than the strange hadron masses. The strange mesons and baryons produced

are also not present at the beginning of the collision, they should be cooked in the

reaction in some way, therefore the study of strangeness production provide essential

information about the physical environment created in the collisions.

The strange particle properties make them also interesting, they are all unstable

particles living very short time before decaying into stable particles. The decay

channels and production rates are of considerable interests because they should reflect

the dynamics of the strong interaction.

Since the dynamics of flavour production in colour confinement processes is one

of the big open questions in particle physics, the production of strange hadrons in

high energy reactions provides an extremely valuable study, so the mechanism of

strangeness production has attracted considerable attention, both in perturbative

and non-perturbative regimes. The study of the hadronization process of strange

particle production (an other particles in general) bring us towards a deeper under-


standing of the strong forces responsible of the confinement.

The rate of strange quark production as compared to production rates for light up

or down quarks depends on the energy density in the colour field providing therefore

a measurement of the energy density and the string constant, in other words, the

typical scales of space, time and momentum transfer involved in the confinement

process.

The phonomenologycal models can also be tested by the comparison to strangeness

results from data, and the optimization of their parameters can be performed. This

is very important since due to our limited knowledge some tests rely strongly on

phenomenological models only.

So far, the Lund string model which provides a rather convincing phenomenology

of hadron production in general, and of strange particle production in particular, uses

the strange to light flavours ratio as a natural explanation calling it, the strangeness

suppression factor λs (see also subsection 1.3.2).

Studies of the strangeness production cross section in different regions of the

phase space have been compared to simulation based on the Lund string model, but

certainly no unique λs describes the data perfectly. What has been found is that a

λs value between 0.2 - 0.3 gives a surprisingly good description, not only of the inclu-

sive strange-particle production, but also of correlations between strange particles,

being the only models of baryon production which have survived the experimental

tests including as well the diquark strangeness factors to assume occasional diquark-

antidiquark pair production in the confinement process to explain the formations of

baryons.

The studies of different ratios providing rather direct measurement of λs, λqq

and/or λsq, as the strange to non-strange ratio: K0S /π, Λ/p, strange to non-strange

charmed mesons and strange to non-strange bottom mesons can also provide good

information but no experimental data is available for all of them.

The same suppression factor is expected to describe both the meson and the

baryon sector, however a perfect determination of λs requires knowledge of the cross

2.3. WHY STRANGENESS STUDIES ARE IMPORTANT? 21

sections and determination of all resonances feeding into stable hadrons which is very

difficult and is not yet fully complete.

The availability of data from different collision types is an advantage for the

strangeness production studies and MC tests due to the differences in the physics

escenarios, but also the compatibility among them in some regions. At the end the

comparisons can test the strangeness universality if all methods yield the same λs.

The particle production in pp collisions at a given√

spp compared to e+e− anni-

hilation at√

s =√

spp/2 have not shown drastic differences in the strange-particle

production rates.

The e+e− annihilation advantage is the detection of the baryon polarization be-

cause the configuration of the colour field is much better known, providing a further

excellent test of string models. Baryon production is best studied in processes with-

out incident baryons, such as this case, since the strange diquark is hence more

strongly suppressed than a strange quark.

The heavy ion collisions also play important roles in many aspects, for instance an

enhancement of the strange particle production in nucleus-nucleus collisions relative

to proton-proton reactions have been established, finding that it depends on the

strangeness content of the particle type, that is the reason of investigations of the

energy and system size dependence of strangeness production. The enhancement was

one of the first suggested signatures for quark gluon plasma QGP formation [29].

Another important point that makes the strange particle analysis interesting

is the search for exotic states as pentaquarks (states with more quarks than the

conventional qqq and qq states) and glueballs (e.g. looking for glueball decaying to

K0SK0

S states).

The particle data group [11] lists a number of unestablished resonances, such

as Θ+ state whose signal has been reported in previous experimental studies [30]

looking for decaying modes including K0S particles. In the same aspect some other

particles for instance D0, Λc and K∗ also have K0S mesons in their decay modes, so

a good selection of the K0S mesons can help to the reconstruction and study of these


heavy particles.

Other possible studies include the strangeness content of the pomeron in diffrac-

tive DIS and the determination of the strange structure function F2(s).

2.4 Previous strangeness production studies

Several studies have been done since many years ago in the strangeness field

looking for mesons, baryons, resonances and even exotic signals. Not only at HERA

ep experiments, but also in pp, heavy ions and e+e− collisions at either linear or ring

colliders at different center of mass energies and regions of phase space.

2.4.1 At e+e− colliders

The DELPHI detector at LEP presented results on inclusive production rates

per hadronic Z decay of Σ− = 0.081 ± 0.010 and Λ(1520) = 0.029 ± 0.007. The

total production rates of vector, tensor and scalar mesons and of baryons follow

phenomenological laws related to the spin, isospin, strangeness and mass of the

particles. This statement was confirmed by other LEP experiments (ALEPH, L3 and

OPAL). In the same study, the ratio Λ(1520)/Λ production increases with increasing

scaled momentum xp. A similar behaviour was found for the ratio of tensor to

vector meson production, f2(1270)/ρ0 but no increase was seen for f0(980)/ρ0 and

a±

0 (980)/ρ± [31]. The strange pentaquark search was performed by the DELPHI

collaboration. None of the states that were searched for was found. Upper limits

were established at 95% CL on the average production rates of such particles and

their charge-conjugate states per hadronic decay.

The π0, η, K0S and charged particle multiplicities were determined for quark and

gluons jets by OPAL collaboration. The multiplicity enhancement in gluon jets was

found to be independent of the studied particle species. The measurement of charged

particle multiplicity in strange flavoured Z0 decays gave < ns >= 20.02 ± 0.13(stat.)

+0.39−0.37 (syst.), while the strangeness factor λs determined was 0.422 ± 0.049 (stat.) ±

2.4. PREVIOUS STRANGENESS PRODUCTION STUDIES 23

0.059 (syst.) [32].

The L3 collaboration measurement of the Λ and Σ0 cross sections at center of

mass energies from 91 GeV to 218 GeV by the processes γγ → ΛΛ and γγ →Σ0Σ

0were extracted as function of the center of mass energy and compared with

CLEO collaboration results, as well to quark-diquark model and three quark model

predictions [33]. Other analysis provided the average number of < NΣ+> + <

NΣ+>= 0.114 ± 0.011 (stat.) ± 0.009 (syst.) and < NΣ0

> + < NΣ0>= 0.095

± 0.015 (stat.) ± 0.013 (syst.) finding that JETSET, HERWIG and ARIADNE

predictions subestimated the measurements [34].

The measurement of inclusive production of the Λ, Ξ− and Ξ∗(1530) baryons in

two-photon collision with the L3 detector were described by PYTHIA and PHO-

JET Monte Carlo programs, the comparison to e+e− annihilation processes provides

evidence for the universality of fragmentation function in both reactions; while the

search for inclusive production of the pentaquark Θ+(1540)→ pK0S showed no sig-

nal [35].

The CLAS collaboration at Jefferson laboratory presented a work with main

goal of measuring observables related to the propagation of a quark struck by the

virtual photon from DIS through cold nuclear matter and compared with quark

propagation through hot QCD matter, or quark gluon plasma (QGP) formed in

relativistic heavy ion collisions at RHIC. That work presented for the first time

results for K0S hadronization plotting the multiplicity ratios of K0

S over DIS events

versus the energy fraction z [36].

2.4.2 At pp and heavy ions collisions

The KAOS collaboration with CC and AuAu collisions at 1-2 GeV where the

kaon emission is a rare process, reported studies of K+ and K− particle production,

showing a dependence on the mass number A of the colliding system, as well as

differences between the K+ and K− cross sections σ per A5/3. The same conclusion

was made for the same particle at different kinetic energies for three different systems


and various beam energies [37].

The FOPI detector studying nuclear matter at high temperatures/high density in

the heavy ion collider GSI in SIS have studied Λp, Λ, K0, φ, Σ∗(1385) and K∗(892).

The inclusive K0 cross section results as function of the target nucleus A after using

π− beam against target nuclei C, Al, Cu, Sn, and Pb, showed an increase at higher

A values [38] and confirming the KAOS collaboration results.

The HADES collaboration also made measurements of strangeness (K+,K−, Λ,

ρ, K0S and Ξ particles) in Ar+KCl system at 1.756A GeV. The results of measured

yields and slopes of the transverse mass of kaons and Λ agrees with KAOS and

FOPI studies [39]. An effective temperature of the kinetic freeze-out of TEff =

92.0 ± 0.5 ± 4.1 MeV [40] is achieved for the K0S .

The CERES studied the K0S yield at midrapidity dN/dy and transverse momen-

tum distributions in central PbAu collisions at top SPS energy [41]. The results were

compared to NA49 [42] and NA57 [43] measurements. An agreement with NA57 K0S

was found in the overlapping rapidity bins within errors.

The PHENIX (pp) [44] and the STAR (AuAu) [45] collaborations at RHIC with√

200 AGeV center of mass energy have measured the ratio of K/π giving a value

between 0.1 - 0.5 and showing very similar results at low pT although a slight hint of

strangeness enhancement (around 20%) is indicated in nucleus collision relative to

pp collisions. The same is expected at LHC [46].

The NA49 collaboration at SPS have also identified K∗(892), K±, ρ, Ξ and Ω

particles [47] and measured the K∗/K± ratio as function of the average number of

wounded nucleons Nw and the resonance lifetime cτ ; while another paper from the

STAR collaboration colliding CuCu and AuAu at√

s =62 GeV, presented the mid-

rapidity dN/dy for K0S , Λ, Ξ and Ω particles and also mid-pT results of the Λ/K0

s

ratio, concluding that the centrality dependance of dN/dy per < Npart > has similar

trends to a parametrisation on the fraction of participants that undergo multiple

collisions. The ratio RAA = (dNAA/dy)/(dNpp/dy) for K0S showed to be greater than

the same ratio for π, providing evidence for parton flavour conversions in heavy-ion

2.4. PREVIOUS STRANGENESS PRODUCTION STUDIES 25

collisions [48].

Other studies with pp collisions have tried to determine the total cross section of

still scarce reactions as pp → nK+Σ+, pp → nK+Σ0 and pp → nK+Λ [49] including

contributions from previously ignored ∆∗(1620) and N∗(1535) resonances. They

shown that these resonances play dominant roles for strangeness production in pp

collisions.

At this section one also ask about the new LHC age, although it consists of

four experiments only ALICE has planes of strangeness studies (in part because

the detector design allows it), a lot of prediction was done concluding the easy

and clear identification of K0S, Λ, Ξ, Ω particles and some resonances [50] but no

measurement are public until today. It is, however, natural to expect that in the

high energy-density phase (quark gluon plasma, QGP) up, down and strange quarks

have similar populations and play equivalent roles. RICH results didn’t confirm that

but it could becomes a good approximation at LHC energies at QGP. Maybe the

expected enhancement of strange anti-baryon production, as proposed by Muller and

Rafelski [29] will be observed.

Can we expect that more final-state strange particles are produced with larger

transverse momenta and pQCD is going to provide more precise predictions?. The

role of strangeness will change at the LHC energies? Do the s quark behave as light

u and d quarks and does charm appear as the first massive flavour?. These and other

questions can find answer in the following few years, being a good reason to continue

with strangeness studies.

2.4.3 At ep colliders

The HERA experiments, HERMES, HERA-B, ZEUS and H1, have also done

measurements of several strange particles, mainly of K0S meson, Λ, Λ baryons, K0

s K0s

and baryonic resonance production.

The fixed target HERA-B experiment measured the cross section rates of K0S , Λ

and Λ [51], K∗0, K∗0

and ρ mesons using C, Ti and W as target materials showing


a power law dependence with the atomic mass of the target. And also reporting a

smaller production of K∗ and K∗0

compared with K+ and K− [52].

The HERMES detector showed that s quarks of Λ, Λ originate predominantly

from s pair production from γ [53].

The Zeus experiment have made a high statistics study of the K0s K

0s system us-

ing the full HERA II data set in the phase space pT (K0s ) ≥ 0.25 GeV and |η| ≤ 1.6.

A number of 672418 K0s K

0s pairs coming mainly from photoproduction were identi-

fied, reporting an observation of states at 1537 MeV and 1726 MeV consistent with

f ′

2(1525) and close to f0(1710), also an enhancement near 1300 MeV which may arise

from the production of f2(1270) and/or a02(1320) [54]. Agreement with the measure-

ments done by L3 [55] and TASSO [56] collaborations at γγ → K0s K

0s was found.

The H1 collaboration have not confirmed these results since no paper or thesis of

these measurements exist until now.

The pentaquark searches at Zeus have looked for baryonic states decaying to

K0S p and K0

S p [57]; e.g., the pentaquark Θ+(uudds) (reported for fixed-target experi-

ments [30]). They find a peak with 221±48 events at 1521.5 ± 1.5(stat.)+2.8−1.7(syst.) MeV

for Q2 ≃ 20 GeV2 providing further evidence for the existence of a narrow baryon

resonance consistent with the predicted Θ+ pentaquark state. Another study at

Q2 >1 GeV2 for Ξ−π−, Ξ−π+ decay channels [58] by ZEUS also gives a clear signal

for Ξ0(1530) → Ξ−π+, but no other signal at higher masses (Ξ−−

3/2 and Ξ+3/2) was

observed. The H1 studies of these resonances are presented in the subsection 2.5.1.

Concerning measurements of the K0S and Λ production, baryon-antibaryon asym-

metry, baryon to meson ratio and strange to light hadrons ratio: The results of

ZEUS in the phase spaces corresponding to photoproduction (Q2 ≃ 0) and DIS

(2< Q2 <25 GeV2 and 25 GeV2 < Q2) collected at√

s = 319 GeV compared to

different ARIADNE and PYTHIA MC models [59] conclude that the DIS results are

reproduced by ARIADNE with λs = 0.22 in gross features, while PYTHIA describes

the cross section as functions of pT and η but doesn’t for x dependence. No Λ - Λ

asymmetry is found. The strange to light quarks ratio is in agreement with e+e−

2.5. PREVIOUS H1 RESULTS OF STRANGENESS AT LOW Q2 27

results but the baryon to meson ratio is larger that e+e− measurements.

The H1 experiment has very nice and recent results of the K0S and Λ production

rates at DIS low Q2 which can be found at references [60], [61] and [62]. The last

published results are discussed extensively in the subsection 2.5.3. The first mea-

surement of the K∗(892) vector by the H1 collaboration at low Q2 is presented in

the subsection 2.5.2.

2.5 Previous H1 results of strangeness at low Q2

The most important studies carried out by the H1 experiment involving the identi-

fication of K0S meson or other strange particles are the search of predicted resonances

as Θ+ → K0S p± and Ξ0(1530) → Ξ−π+, the identification of K∗(892) meson and the

analysis of K0S meson and Λ baryon. All of them through the analysis of data at low

Q2.

2.5.1 Search of resonances

Figure 2.4: Invariant mass spectra of a) K0S candidates reconstructed by the decay

mode π+π− and b) Θ+ candidates decaying to K0S p±, no signal is observed in the

mass range of 1.48 to 1.7 GeV.

b)


A search of the hypothetical baryon Θ+ in the decay channels K0S p± as ob-

served by several fixed-target experiments is done at H1, in the phase space 5<

Q2 <100 GeV2 and 0.1< y <0.6. The data were taken during the years 1996-2000

(HERA I1) with a luminosity of 74 pb−1.

The K0S is reconstructed by looking for π± tracks coming from a secondary vertex

in the central part of the detector. The invariant mass distribution fitted to two

Gaussian functions is showed in Figure 2.4 a). A number of 133,000 K0S candidates

are obtained after subtracting the background.

The combination of the K0S candidate with the proton candidates gives the recon-

struction of Θ. The detailed procedure is explain in [63]. The mass range considered

for the search is 1.48 to 1.7 GeV since the reported masses are between 1520 and

1540 MeV. No signal for the resonance Θ+ production is observed in the studied

decay modes as shown in the mass distribution spectra in Figure 2.4 b) where the

corresponding upper limits are also shown.

The analysis was repeated at large Q2 and low proton momentum region in which

ZEUS collaboration made its observation but no evidence was found.

The analysis of baryonic resonances and their antiparticles X−− and X0 in the

mass range 1600 to 2300 MeV is also carried out with the H1 detector. The search

is perfomed in the region defined by 2< Q2 <100 GeV2 and 0.05< y <0.7 using data

taken in 1996-1997 and 1999-2000 with L = 100.5 pb−1. The particle decay modes

are X−− → Ξ−π− → [Λπ−]π− → [(pπ−)π−]π− and X0 → Ξ−π+ → [Λπ−]π+ →[(pπ−)π−]π+.

The identification of these particles is done first by looking for the Λ (Λ) baryon

by their p (p) and π− (π+) daugther signals, second it is made a combination of the Λ

candidate with negatively charged track assumed to be a pion and third, the X−−/0

candidates are formed by combining each of these Ξ− candidates with an additional

pion track; for extended explanation of the reconstruction, see references [64] or [61].

In Figure 2.5 one can see the resulting invariant mass spectra for the neutral

1The description of the HERA I and HERA II data can be found in the chapter 3.


Figure 2.5: Invariant mass distribution of the combinations a) Ξ−π+, b) Ξ+π−, c)Ξ−π− and d) Ξ+π+ with the fit to signal and background. A clear signal of theΞ0(1530) baryon is observed for the neutral combinations in the mass range of 1600to 2300 MeV.

a) b)

c) d)


Ξ−π+ and Ξ−π+, and the doubly charged combinations Ξ−π− and Ξ+π+. In the

neutral particle distributions, a peak is observed corresponding to the established

Ξ0(1530) state. A fit using a Gaussian function for the signal and p1(M − mΞ −mπ)p2 ∗ (p3 +p4M +p5M

2) for the background is applied to the mass spectra yielding

a total of 171 ± 26(stat) Ξ0(1530) baryons in the mass range of 1600-2300 MeV. In

the other hand, for the doubly charged combinations no signal is found.

The results showed compatibility with ZEUS measurement at 2< Q2 <100 GeV2

looking for the same decay modes.

2.5.2 Analysis of K∗(892) meson production

The H1 collaboration has made important progress in the K∗(892) vector meson

cross section measurement both in the laboratory and in the hadronic center of

mass system (γ∗p) frames. The meson was studied looking for the decay channel

K∗(892) → K0s π

± → (π+π−)π± with BR = 23.06% in the data period 2005-2007

with a corresponding accumulated luminosity of 302 pb−1. The events where selected

in the phase space defined by 5< Q2 <100 GeV2, 0.1< y <0.6, -1.5< η(K∗) <1.5

and pT (K∗) > 1 GeV. The detailed selection criteria of the kinematics, the electron,

the tracks, the K0S and the K∗ can be found in reference [65].

The number of K∗(892) are extracted from a fit to the invariant mass of the

Breit Wigner function for the signal description and the p1(m0 − (mK0s +mπ

)p2) ∗Exp(p3m + p4m

2 + p5m3) function for the background. At the end, 80000 K∗±

candidates are identified after the background subtraction and used for the cross

section determination:

σvis = 7.36 ± 0.087(stat.) ± 0.88(syst.) nb. (2.5)

The differential cross section measurement of the K∗(892) in the laboratory and

γ∗p frames are compared to the Monte Carlo simulation programs Django and Rap-

gap, both simulated with matrix elements plus colour dipole model (CDM) and par-

ton showers (MEPS) respectively convoluted with CTEQ6L parton density function


[GeV]T

p1 10

[pb/

GeV

]T

/dp

σd

1

10

210

310

410

510 H1 Data (Prel.)Djangoudcbs

X)±*

eK→ cross section in DIS (ep ±*

Inclusive K

H1 PreliminaryHERA II

5η

-1 0 1

[nb

]η

/dσd

0

1

2

3

4

5H1 Data (Prel.)Djangoudcbs

X)±*


Inclusive K


]2 [GeV2Q10 210

]2 [p

b/G

eV2

/dQ

σd

1

10

210

310


X)±*


Inclusive K


[GeV] pγW100 150 200 250

[pb/

GeV

] pγ

/dW

σd

50

100

H1 Data (Prel.)Djangoudcbs

X)±*


Inclusive K


Fx0 0.2 0.4 0.6 0.8 1

[pb]

F/d

xσd

210

310

410


X)±*


Inclusive K


]2 [GeV*2TP

0 20 40 60 80 100

]2 [p

b/G

eV*2 T

/dP

σd

-210

-110

1

10

210

310


X)±*


Inclusive K


Figure 2.6: The K∗ production cross section as functions of transverse momentumpT , pseudorapidity η and photon virtuality Q2 laboratory variables and center ofmass energy Wγp, x-Feynmann xF and transverse momentum squared P ∗2

T in thehadronic center of mass system frame. The Django model describes the data ingeneral features but fails to describe the shape of the cross section as function of η.The contribution of quark flavours are presented in order to study the productionmechanism of strange particles.


(PDF) and interfased to Lund string fragmentation model with strangeness suppre-

sion factors set to ALEPH collaboration tunning. Both, Django and Rapgap models,

describe the data very well in overall features but fail to describe in detail the shape

of η production. The plots of the measurements are presented in Figure 2.6 where

the contribution of the quark flavours to the production studied with Django are

displayed.

The contribution of different flavours to the cross section can provide clues to

the strange particle production mechanisms. It is observed that K∗ coming from ud

quarks are mainly from fragmentation; those coming from cb quarks belong mostly

to heavy hadron decays (heavy quarks created by BGF) and give the second highest

contribution; while the K∗ from s quark (mainly due to the hard subprocess) cor-

respond to only the 20% of the total cross section prominently at high values of xF

and p∗T . It was observed that the xF variable provides good sentitivity to the flavour

composition studies.

2.5.3 K0S and Λ studies at low Q2

The H1 collaboration has recently published [66] the measurement of the K0s ,

Λ and Λ cross sections together with the ratios of baryon to meson and meson to

charged particles using DIS events at the phase space defined by 2 < Q2 < 100 GeV2,

0.5 < pT < 3.5 GeV, -1.3 < η < 1.3 using HERA I data with L = 50 pb−1. The

decay channels used for the identifications are K0S → π−π+ with BR ≃ 69.2% and

Λ → pπ with BR ≃ 63.9%.

The measurements are presented in the laboratory frame as a function of Q2, η

and pT and in the Breit frame (appendix E) in the current and target hemispheres

as a function of the momentum fraction xBFp and the K0

S transverse momentum

pBFT . The results were compared to Django (CDM) and Rapgap (MEPS) models

with λs = 0.2, 0.286 and 0.3 for CTEQ6L, H12000LO and GRV94 parton density

functions.

The 213,000 K0S candidates taken from the fit to the invariant mass distribution,


) [GeV]-π +πM(0.4 0.5 0.6

En

trie

s p

er

2M

eV

0

5000

10000

15000

H1

+π -π → s0K

H1 Data

Figure 2.7: The K0S invariant mass distribution from data with statistical uncertainty

denoted with the error bars for each point.

showed in Figure 2.7, are used for the measurement of the inclusive K0S cross section

in the visible range, giving:

σvis = 21.28 ± 0.09(stat.)+1.19−1.23(syst.) nb.

In analogy, the inclusive cross section of both the 22000 Λ and 20000 Λ identified

is measured as σvis = 7.88 ± 0.10(stat.)0.450.47(syst.) nb.

Figures 2.8 and 2.9 show the differential cross section of the K0S mesons as a

function of laboratory and Breit frame variables, respectively. The MC over data

ratio are plotted in the bottom part of each distribution. It shows the comparisons

to CDM and MEPS. It seems that CDM with λs = 0.3 makes a good description of

the differential cross section as a function of Q2, x, η and pT , but finds difficulties

to describe the shape of η and low pT . Whereas the Breit frame calculations agree

with CDM model taking a strangeness factor λs = 0.3.

Similar plots for Λ were obtained and can be seen in references [66] and [67],

CDM with λs = 0.3 behaves more like data in this case but one should not forget that

sensitivity to λqq and λsq is expected. The Λ asymmetries, AΛ = (σΛ−σΛ)/(σΛ+σΛ),


]2 [n

b/G

eV2

X)/d

Qs0

e K

→(e

p σd

1

2

3

4

5

6

7 H1 H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

]2 [GeV2Q10 210

Theo

ry /

Dat

a

0.81

1.2

X)/d

x [n

b]s0

e K

→(e

p σd

310

410

510 H1 H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

x

-410 -310 -210

Theo

ry /

Dat

a

0.81

1.2

[nb/

GeV

]T

X)/d

ps0

e K

→(e

p σd

20

40H1 H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

[GeV]T

p0.5 1 1.5 2 2.5 3 3.5Th

eory

/ D

ata

1

1.5

[nb]

η X

)/ds0

e K

→(e

p σd

2

4

6

8

10 H1

H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

η-1 -0.5 0 0.5 1Th

eory

/ D

ata

1

1.5

Figure 2.8: The differential production cross sections for K0S in the laboratory frame

as a function of the four-momentum of the virtual photon Q2, Bjorken scaling variablex, K0

S transverse momentum pT and K0S pseudorapidity η. The theory/data ratios

on the bottom show the comparison to the model predictions. Inner (outer) errorbars for statistical (total) uncertainties.


[nb/

GeV

]Br

eit

T X

)/dp

s0 e

K→

(ep

σd

5

10

15

20

25 H1

target region

H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

[GeV]BreitT

p0.5 1 1.5 2 2.5 3 3.5 4Th

eory

/ D

ata

1

1.5

[nb]

Brei

tp

X)/d

xs0

e K

→(e

p σd

1

2

3

4

5

6

7 H1

target region

H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

Breitpx

0 5 10 15 20Theo

ry /

Dat

a1

1.5

[nb/

GeV

]Br

eit

T X

)/dp

s0 e

K→

(ep

σd

1

2

H1

current region

H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

[GeV]BreitT

p0 0.5 1 1.5 2 2.5 3Th

eory

/ D

ata

0.81

1.2

[nb]

Brei

tp

X)/d

xs0

e K

→(e

p σd

2

4 H1

current region

H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

Breitpx

0 0.2 0.4 0.6 0.8 1Theo

ry /

Dat

a

0.81

1.2

Figure 2.9: The differential K0S production cross sections in the Breit frame as a

function of pBCT and xBC

p in the target and current hemisphere. The theory/dataratios on the bottom show the comparison to the different model predictions. Inner(outer) error bars for statistical (total) uncertainties


measured in the laboratory and the Breit frames are consistent with zero showing no

evidence of baryon number transferred from the proton beam to the Λ final state.

The meson to charged particles ratio with an averaged measurement of:

σvis(ep → eK0SX)

σvis(ep → eh±X)= 0.0645 ± 0.0002(stat.)+0.0019

−0.0020(syst.)

was calculated differentially as shown in Figure 2.10 for the laboratory frame as

function of Q2, x, η and pT . The parameter λs is expected to be less model dependent

here. The ratio strongly rises with increasing pT but remains approximately constant

as a function of all the other variables. The models describe reasonably well the ratio

but none is able to describe the shape, especially of η and low pT .

The measured baryon to meson ratio average is

ep → eΛX

ep → eK0SX

= 0.372 ± 0.005(stat.)+0.011−0.012(syst.). (2.6)

The CDM model agrees with data but not completely for the differential measure-

ment in the laboratory frame, no model dependence was found in the Breit frame

since no sensitivity to λs is expected but λqq and λsq can contribute.

The comparison between three different proton PDFs: CTEQ6L, GRV-94 (LO)

and H1 2000 LO, with λs = 0.286 does not show any dependence.


e h

X)

→(e

pσ

X)/d

s0 e

K→

(ep

σd

0.04

0.06

0.08

0.1

0.12

H1H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

]2 [GeV2Q10 210

Theo

ry /

Dat

a

0.81

1.2

e h

X)

→(e

pσ

X)/d

s0 e

K→

(ep

σd

0.04

0.06

0.08

0.1

0.12

H1H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

x-410 -310

Theo

ry /

Dat

a0.8

1

1.2

0.5 1 1.5 2 2.5 3 3.5

e’ h

X)

→(e

pσ

X)/d

s0 e

’ K→

(ep

σd

0.04

0.06

0.08

0.1

0.12

H1

H1 Data=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

[GeV]T

p0.5 1 1.5 2 2.5 3 3.5

Theo

ry /

Dat

a

0.81

1.2-1 -0.5 0 0.5 1

e h

X)

→(e

pσ

X)/d

s0 e

K→

(ep

σd

0.04

0.06

0.08

0.1

0.12

H1H1 Data

=0.3)sλCDM (

=0.22)sλCDM (

=0.3)sλMEPS (

=0.22)sλMEPS (

η-1 -0.5 0 0.5 1

Theo

ry /

Dat

a

0.81

1.2

Figure 2.10: The differential K0S mesons to charged particles cross sections ratio

as a function of the four-momentum of the virtual photon Q2, the Bjorken scalingvariable x, the transverse momentum pT and the pseudorapidity η in the laboratoryframe. The theory/data ratios on the bottom show the comparison to the modelpredictions. Inner (outer) error bars for statistical (total) uncertainties


Chapter 3

HERA and the H1 Detector

The electron-proton collider HERA, located at DESY in Hamburg, Germany, of-

fers the opportunity to study the structure of the proton. HERA consists of four

different experiments spaced evenly along its circumference. One of those experi-

ments, the H1 detector, provided the data analysed in this work. H1 is composed

of several kind of detectors, fixed in a whole unit, designed to measure the particles

properties.

A brief introduction to the HERA machine and the H1 detector components

relevant for the studies presented on this thesis can be found here.

3.1 The HERA collider

The electron-hadron accelerator ring, HERA1, was built at the German electron

synchrotron laboratory, DESY2, in Hamburg, Germany. It consists of two indepen-

dent rings working as accelerators and storing proton and electrons with a center of

mass energy of 319 GeV.

In Figure 3.1 a schematic picture of HERA collider and the pre-accelerator PE-

1Hadronen Elektronen Ring Anlage2Deustches Elektronen SYnchrotron

39

40 CHAPTER 3. HERA AND THE H1 DETECTOR

TRA3 can be found. This pre-accelerator is located at the south-west and it is

amplified in Figure 3.1 b). The performance of the accelerator begins with injection

of protons4 with an energy of 50 MeV from the linear accelerator, H−-linac, to the

DESY III ring, where they are accumulated and accelerated until having 70 bunches

with 7.5 GeV. Then, one by one are sent to the PETRA ring to be accelerated up to

40 GeV, to finally be transferred to the HERA ring. HERA operates with 180 circu-

lating bunches of protons, every one of them consisting of approximately 1010-1011

protons, separated in time by 96 ns and accelerated to an energy of 920 GeV.

Hall North

H1

Hall East

HERMES

Hall South

ZEUS

HERA

HERAhall west

PETRA

cryogenichall

Hall West

HERA-B

magnettest-hall

DESY II/IIIPIA

e -linac+

e -linac-

-H -linac

NWN NO

O

SOSW

W

proton bypass

p

e

ep

VolksparkStadion

360m

360m

R=7

97m

e

p

Trabrennbahn

Figure 3.1: a) The HERA accelerator and b) the PETRA pre-accelerator circumfer-ences. The four experiments around HERA: HERA-B, H1, HERMES and ZEUS areindicated in a) together with the traveling direction of the electron e and proton pbeams.

a) b)

The electrons (or positrons) acceleration begins at the e− (e+)-linac accelerator,

the electrons are injected from there to the DESY II ring, where they are accelerated

from 450 MeV to 7 GeV. After the storage of 70 bunches is completed, they start

to be sent to PETRA for their acceleration up to 14 GeV. At the end, 180 bunches

3Positron Elektron Tandem Ring Anlage4The protons are taken from hydrogen ions

3.1. THE HERA COLLIDER 41

of electrons are injected to HERA until they get an energy of 27.5 GeV, separated

by the same time interval as proton bunches. Sometimes, some bunches, called pilot

bunches, are left empty to be used for the background estimation, of protons colliding

with the beam pipe or residual gas.

The proton bunches lifetime easily exceeds 24 h, but the lifetime of the electron

bunches is limited to about 6 h (the lifetime for positrons is approximately a factor

of 2 higher). Both electrons and positrons are more difficult to keep circulating due

to the synchrotron radiation.

The HERA accelerator ring has a circumference of 6.3 km where superconduct-

ing dipole and focusing quadrupole magnets are distributed to guide the particles

trajectories and to keep the bunches positionally stables. Between the quadrupoles,

∼12 m of free space is available for a detector. The beams pass inside a 190 mm

inner diameter beam pipe with a wall of 150 µm Aluminium on the inside backed by

2 mm carbon fiber. The beam pipe is cooled with nitrogen gas and kept in vacuum

conditions. It crosses the detector in its center at a height of 5.9 m above the floor

level at an inclination of 5.88 mrad.

Around HERA, four experiments are located: HERMES, HERA-B, ZEUS and

H1. Their locations are graphically shown in Figure 3.1 a). The electrons and

protons, traveling to the right and left hand sides respectively, are made to collide

head on (as in H1 and ZEUS detectors) or against a target (as in HERMES and

HERA-B detectors) every 96 ns or 10.4 MHz. HERMES, HEra MEasurement of Spin,

is dedicated to spin studies of the proton, HERA-B is interested in CP violations in

B0 − B0 systems and, ZEUS and H1 study the proton structure.

An important characteristic of any accelerator operation is the produced lumi-

nosity which gives directly the number of events per second for a cross section of

1 cm2 (units of cm−2s−1). The instantaneous luminosity L, can be calculated with

the revolution frequency f of the bunches, the number of protons Np and electrons


Ne per bunch and the beam radii σx and σy of the bunches at the crossing point:

L =f ∗ Ne ∗ Np

2π ∗√

2σx ∗√

2σy

, (3.1)

due to the uncertainty in the beam collimation the luminosity is measured as ex-

plained in the subsection 3.2.3.

The luminosity is also related to the effective cross section σ as: dN/dt = Lσ.

The accumulated luminosity at a period T of time is denoted as:

L =

∫

T

Ldt (3.2)

day

Prod

uced

by H

ERA

[pb-1

]

0 100 200 3000

100

200 2002200320042005200620072007 low-E run2007 mid-E run

Figure 3.2: Accumulated luminosity by HERA II collider in pb−1 vs number of daysfor six years of operation. In 2007 two periods of several months were dedicated tothe operation of the machine at low and middle energies.

The HERA operation time is divided in two periods called HERA I and HERA II.

HERA I corresponds to data taken from 1992 to 2000 while HERA II goes from 2002

to 2007. The separation responds to the improvements made to the accelerator in

3.2. THE H1 DETECTOR 43

2001. Several super-conducting quadrupole magnets where installed, improving the

focusing of the beams and consequently increasing the luminosity by a factor of 4

to 5. In Figure 3.2 is possible to see the produced luminosity by HERA in pb−1 per

year. The HERA accelerator ended its performance in summer 2007.

3.2 The H1 detector

The H1 experiment [68] is located in the northern side of the HERA ring, at 20 m

underground. The detector measures 12 x 10 x 15 m3 and its weight is 2,800 tons. The

coordinate system of H1 is right-handed with the origin settled up on the interaction

vertex (also called nominal point), the x axis points to the center of HERA, y pointing

up and the z axis defined by the incoming proton beam direction (from right to left

hand side in Figure 3.3). In polar coordinates, the azimuthal angle φ rests in the xy

plane being φ = 0 over the x axis while the polar angle θ is zero on the positive z

axis. The pseudorapidity is defined as η = −ln [tan(θ/2)].

Figure 3.3 presents a longitudinal cut of the H1 detector with the protons and

electrons coming into the detector from the right and left hand side, respectively.

The H1 detector is composed by several kind of sub-detectors in order to measure

the energy, momentum and charge of the particles produced during and after the

ep collisions. The difference of energy between electrons and protons makes that

most of the particles are scattered in the outcoming proton direction or the so called

forward region. This is the reason why the H1 detector is considerably more massive

and highly segmented in that direction.

The detector is arranged as follows: immediately outward from the interaction

vertex is the tracking system, consisting of the Central Silicon Tracker (CST), a

central (CJC, COZ, CIZ, COP and CIP) and a Forward Tracking System (FTS)

used for the trajectory particle reconstruction. Two calorimeters surrounding the

trackers are the liquid argon calorimeter (LAr Cal) in the central and forward region,

and the scintillator spaghetti calorimeter (SpaCal) in the backward region, both


Figure 3.3: Cut along the z beam axis of the H1 detector. The components ofthe tracker, calorimeter and muon systems are indicated. The separation in cen-tral, forward at the left hand side and backward to the right hand side can be alsoschematically seen.


calorimeters have electromagnetic and hadronic sections ideal to measure the energy

of the particles. Housing all these systems is a superconducting solenoidal cylindrical

magnet with a diameter of 6 m and a length of 5.75 m which provides a homogeneous

magnetic field of 1.16 T parallel to the z axis. This magnetic field makes that charged

particles produced in the collision move in an helical trajectory. The projection of

this trajectory in the xy plane yields a circle with radius r = 1/pt where pt is

the transverse momentum of the particle. The iron return yoke of the magnet is

laminated and filled with limited streamer tubes.

The small fraction of hadronic energy leaking out the calorimeter and the muon

tracks are measured by the central muon identification system (CMS) placed af-

ter the solenoid coil. Stiff muon tracks in the forward direction are analysed in a

supplementary toroidal magnet sandwiched between drift chambers. See Figure 3.3.

An electron tagger located at z = -33 m from the interaction point in coincidence

with a corresponding photon detector at z = -103 m upstream (not shown in Fig-

ure 3.3) detect the tag electrons and photons produced with very small scattering

angle and monitor the luminosity by the Bethe-Heitler process.

The H1 detector, as well as the HERA accelerator, was updated substantially

during the time changing from HERA I to HERA II to cope with the new challenges

at HERA II. The innermost detector regions saw major modifications to accommo-

date the superconducting quadrupoles of HERA II. The new silicon detector system

(Forward Silicon Tracker) completely surrounds the interaction region to significantly

improve vertexing and tracking in conjuntion with the upgraded inner tracking sys-

tem (new Forward Tracker). Combined with upgrades in the trigger (new Time Of

Flight System, new multiwire proportional chamber CIP2k replacing the CIP and

CIZ to overcome the increased non-ep background, an upgraded neural net event

trigger for the second level, a new processing farm for the third level and a new Fast

Track Trigger at the very first level) and data acquisition system (DAQ) to make

best use of the luminosity increase in all physics areas. As well as, the installation

of a new superconducting magnet G0 and GG (see Figure 3.3) to obtain a better


longitudinal polarisation of the electron beam at the interaction point.

Days of running

H1 I

nte

gra

ted

Lu

min

osi

ty /

pb

-1

Status: 1-July-2007

0 500 1000 15000

100

200

300

400electronspositronslow E

HERA-1

HERA-2

day

Acc

umul

ated

by

H1

[pb

-1]

0 100 200 3000

40

80

120

1602002200320042005200620072007 low-E run2007 mid-E run

Figure 3.4: Accumulated luminosity in pb−1 of the H1 detector a) during the HERA I(1992-2000) and HERA II (2002-2007) data taking, indication of the periods withthe machine operating with electrons and positrons are plotted in blue and red, b)the HERA II accumulated luminosity, as function of the number of days, separatedby years.

a) b)

The H1 accumulated luminosity is plotted in the Figure 3.4 a), where can be

seen the comparison between the collected luminosity during HERA I and HERA II

periods, with HERA operating electrons and positrons alternatively. A clear increase

in the accelerator performance can be observed. The plot in Figure 3.4 b) shows the

HERA II period luminosity separated year by year since 2002 to 2007.

This study is done with the data taken from 2004 to 2007 where the integrated

luminosity has a value of ∼ 340 pb−1.

The H1 phase space is pretty wide in x-Bjorken and virtuality Q2 as can be seen

in Figure 3.5, where the comparison to different experiments is presented. The range

of Q2 considered for this analysis lies in the regime of the LHC experiments, ATLAS


Table 3.1: The HERA ep collider characteristics.

HERA I HERA II

e− p e− p

Energy 27.6GeV 920 GeV 27.6 GeV 920 GeV

Total current 52 mA 109 mA 45 mA 110 mA

Number of available bunches 180 180 180 180

Number of bunches in collision 174 174 174 174

Number of particles per buch 3.5 x 1010 7.3 x 1010 4.2 x 1010 10 x 1010

Transverse cross section per buchσx x σy (µm x µm) 192 x 50 189 x 50 112 x 30 112 x 30

Length of the bunch 10 mm 191 mm 10 mm 191 mm

Luminosity 6.5 x 10−3 (nb−1s−1) 17.2 x 10−3 (nb−1s−1)

6.5 x 1030 (cm−2s−1) 17.2 x 1030 (cm−2s−1)

and CMS.

In the next sections a brief description of the most important subdetectors for

this analysis can be found. For more information about the H1 detector, see the

Table 3.1 or consult the reference [69].

3.2.1 Tracker system

The tracker system consists of drift and multiwire proportional chambers detec-

tors, see appendix B, for triggering and the identification of particles by the mea-

surement of their charges, momentum and the reconstruction of their trajectories,

with resolutions of σp/p2 ≈ 3 x 10−3 GeV−1 and σθ ≈1 mrad. The tracking chambers

are built to interfer as little as possible with the passing track.

This system is the main detector at H1, designed for the reconstruction of jets

with high particle densities. Each component of the tracking system was built and


Figure 3.5: Phase space of different experiments presented in x-Bjorken vs. Q2. TheH1 detector has pretty wide range, so that the Q2 considered for this analysis lies inpart of the regime from ATLAS and CMS experiments.

tested separately, then assembled and locked to one mechanical unit to provide pre-

cise alignment relative to outside support, but with electrostatic shielding and inde-

pendent gas volume. A schematic picture of the tracking detectors can be found in

Figures 3.6 and 3.7.

The tracker system is divided in the central (CTD), the forward (FTD) tracker

detectors and the backward proportional chamber (BPC).

The CTD is covered by the central (CST), the forward (FST) and the backward

silicon tracker (BST), the central jet chamber (CJC), the central inner (CIZ) and

central outer z-chamber (COZ), and the central inner (CIP) and central outer (COP)

multiwire proportional chambers.

The CJC is based on two large concentric drift chambers, CJC1 and CJC2, de-

signed for transverse track momentum determination by the signals recorded, in

addition, the specific energy loss dE/dx can be used to improve particle identifica-

3.2. THE H1 DETECTOR 49 @@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀ@@@@@@@@@ÀÀÀÀÀÀÀÀÀ@@@@@@@@@ÀÀÀÀÀÀÀÀÀ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀ @@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ@@@@@@@@@ÀÀÀÀÀÀÀÀÀ@@@@@@@@@ÀÀÀÀÀÀÀÀÀ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀ@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀ013 2 -1 -2 m

0

1

-1

Forward TrackDetector (FTD)

Central Track Detector(CTD)

Central Jet Chamber (CJC)

CJC2

CJC1

COZ COP CIZ CIP

Silicon Tracker

cableselectronics

BDC elm hadrSpaCal

cable distri-bution area

(CDA)

transitionradiators

planars

radials MWPCsCST BST

Figure 3.6: Longitudinal view of the forward and central tracker systems. The CST,CJC, COZ, CIZ, COP and CIP detector locations are shown.

tion. The measurement is complemented by the two thin z drift chambers, CIZ and

COZ, which give better accuracy by measuring the z coordinate of the tracks.

The FTD, electrically isolated from the CTD, has three supermodules covering

a polar angle range of 5 < θ < 25. Each supermodule consists of planar drift

chambers orientated in different wire geometries, a multiwire proportional chamber

(FWPC), a passive transition radiator and a radial drift chamber, all them with

wires strung perpendicular to the beam direction, Figure 3.6. This tracker allows

accuracy in θ, rφ measurements and fast triggering.

The CIP, COP and the FWPC, are used to trigger on tracks coming from a

nominal interaction vertex, providing the first level (L1) trigger decision which is

also used to distinguish between successive beam crossings.

The following subsections will refer in detail the detector components of the

central tracker system.


Figure 3.7: Transversal view of the central tracker system (CTD). The main detec-tors, CST, CJC1, CJC2, CIP2k, COZ and CIP are indicated together with theirradial distances.

3.2.1.1 Central silicon tracker

The central silicon tracker [70], CST, is the nearest detector surrounding the

beam pipe. It was installed in 1997 but updated during the time changing from

HERA I to HERA II. The BST and FST were installed later to complement the

device performance. Its main use is to improve the CJC reconstruction of tracks

relating them to the interaction vertex.

The silicon trackers consist of two radial cylindrical layers of silicon strip detec-

tors, the inner layer with 12 ladders and the outer layer with 20 sensor ladders (each

containing 6 sensors). The CST covers an acceptance of 30 < Θ < 150. Its intrinsic

resolution is σz = 22 µm and σrφ = 12 µm.

3.2.1.2 Central jet chambers

The inner CJC1 and outer CJC2 jet chambers [71] measure the trajectories of

charged particles5, both having a longitude of 2.5 m parallel to the z axis. The CJC1,

5See appendix B for an explanation of the drift chambers performance.


with an inner (outer) radius of 20.3 cm (45.1 cm), has 720 sense wires distributed in

30 azimuthal cells. On the other hand, the CJC2 has 32 sense wires in each of its 60

cells and its inner (outer) radius is 53 cm (84.4 cm). All cells are tilted by about 30

in radial direction, in order that also the tracks with high momentum (low curvature)

can be reconstructed, see Figure 3.7. In fact, the separation of tracks coming from

different bunch crossings is possible to an accuracy of σ ∼ 0.5 ns.

Each cell is composed by three planes of wires, the cathode wires planes marking

the limits of the cell and the anode sense wires plane lying in between. All wires

parallel to the z beam line axis. The diameters of the wires limits the surface field

to ≤ 2 KV/mm.

The jet chambers are closed and filled in the first phase with a gas mixture of

Ar/CO2/CH4 by 89.5/9.5/1.0 %, and Ar/C2H6+H2O by (50/50) + 0.5 % during

the second phase. In this condition, when a charged particle passes through the jet

chambers, the electrons will drift to a velocity of 50 mm/µs−1 towards the anode wires

to induce the current signal which allows the measurement of the hit position in the

xy plane with a resolution of σrφ = 170 µm. Then, comparing the collected charge

at both ends on the wire, the z position can be determined with a precision of σz =

2.2 cm. For a better explanation of the way of charge Q and time t measurements,

read appendix C.

3.2.1.3 Central z chambers

The z central inner CIZ and outer COZ drift chambers measure the z-coordinate

and complement the CJC for the track reconstruction. They are also used for the

trigger of straight tracks pointing to the interaction region.

The CIZ chamber is located between the CST and CJC1, just after the CIP while

COZ is found between the CJC chambers. See figures 3.6 and 3.7. They cover polar

angles of 16 < θ < 169 and 25 < θ < 156, respectively.

The CIZ chamber is a regular polygon with a length of 2.467 m and thickness of

26.5 mm, it is composed by 15 independent ring cells with 4 sense and 3 potential


wires each of them. The gas mixture inside is Ar/C2H6 + H2O at a proportion of

(70/30) + 0.2 allowing a drift velocity of 52 mm/µs and measurement resolutions of

σrφ = 28 mm and σz = 26 µm.

The COZ polygonal chamber is 2.59 m long and 25 mm width, has 24 cells (or

rings), each cell containing 4 sense and 6 potential wires. It has a gas mixture of

Ar/C2H6 + C3H7OH by (48/52) + 1 %, so the drift velocity is 48.5 mm/µs with

accuracy of σrφ = 58 mm and σz = 2.0 µm.

The wires are all tilted by 45 with respect to the normal to the chamber axis.

The first backward nine cells of CIZ are backward tilted but the other six in the

forward direction are tilted forward.

3.2.1.4 Central proportional chambers

There are two multiwire proportional chambers6 (MWPC’s) in the H1 detector:

the central inner (CIP) and the central outer (COP). During HERA II period, the

CIP chamber, together with CIZ, were replaced by a high granularity central inner

proportional chamber (CIP2k) [72] to increase the non-ep background rejection and

to deliver a precise information about the event timing (t0).

The CIP2k chamber has an inner (outer) radius of 15 cm (20 cm) and an active

length of 2.2 m. It is located between the CST and the CJC1. It consists of five

cylindrical detector layers segmented into 16 azimuthal sectors with cathode pad

readout about 2 cm along the z axis. Due to the very fast response to ionizing

particles (depending on the chamber gas and the field strength) this chamber is used

to provide a precise information about the event timing t0 (the typical intrinsic time

resolution is 10 ns) to suppress background events.

The COP detector is located between the CJC1 and CJC2 (Figure 3.6). It is used

in parallel to the CIP2k trigger to suppress tracks with a low momentum transfer

(pt cut) and to the z-vertex trigger to reconstruct the exact vertex in a z region of

± 43.9 cm around the nominal interaction point (σz ≈ 5.5 cm).

6See appendix B for an explanation of the multiwire proportional chambers performance.


3.2.2 Calorimeters

The calorimeters of the H1 detector were designed to identify and provide a precise

measurement of charged and neutral particles, specially the electron parameters of

the DIS events in a wide range of solid angle, as well as jets with high particle

densities. This kind of detector have the purpose of measuring the energy of the

particles by their total or partial absorption.

According to the material of construction they can provide signal such as ion-

ization, as the liquid argon calorimeter in H1, or scintillated light, as the SpaCal

detector.

3.2.2.1 Liquid argon calorimeter

The liquid argon calorimeter [73] (LAr) surrounds the system of tracker detectors

but it is still inside the superconducting coil. It has 1.5 m of thickness active diameter

and measures 7 m of longitude, covering a polar angle range of 4 ≤ θ ≤154 and

4π coverage in φ. The calorimeter is complemented in the forward region (between

the beam pipe and the liquid argon cryostat) by the PLUG, the Spacal and the tail-

catcher system (TC) in the backward direction, to cover the region were hadronic

particles can be leaking out of the detector.

The LAr is segmented in eight wheels each of them divided in φ into eight identical

units in the xy plane. The first two wheels starting from forward region, are two half

rings assembled. The Figure 3.8 presents longitudinal and transversal views of the

LAr calorimeter.

The LAr has a fine granularity for e/π separation (electromagnetic and hadronic

showers) and energy flow measurements as well as homogeneity of response. Each

wheel is divided in an electromagnetic (EM) and a hadronic section (HAD), see

Figure 3.8. The octants are segmented in 45000 cells, where 30000 belong to the EM

and the rest to the HAD part.

A EM cell consists of two lead absorber plates of 2.4 mm interleaved with LAr ac-

tive material interspaces of 2.35 mm. Over each face of the absorber, next to the LAr,


Figure 3.8: a) Longitudinal views of the LAr Calorimeter with the eight wheels di-vided in electromagnetic and hadronic sections. b) Transversal cut of the calorimetershowing one wheel where the separation between electromagnetic and hadronic sec-tions are also indicated, the inclination of the 8 units is visible.

a)

b)


there are circuit planes impressed in G10 (a composite made of glass fiber and epoxy

resin) which have the copper lecture modules (the pads). The electrons produced in

the liquid argon are collected at these plates. Since there is no charge multiplica-

tion, the collected charge is quite small, and the detector requires a preamplifier and

associated electronics for each channel. The chamber must operate at liquid argon

temperatures (80K) and thus requires a cryogenic system (circulation of helium gas).

The hadronic cells has a similar EM structure, an absorber material made of

16 mm (19 mm) stainless steel with sheets connected to high voltage and a double

gap of 2.4 mm liquid argon. The double gap is separated by the G10 plate which

contains the lecture pads.

The liquid argon was chosen because its easy calibration, good stability and

homogeneity in the response. Although the detector is relatively slow, it is stable, is

not adversely affected by the presence of a magnetic field, and is easily segmented.

The detector has uniform sensitivity, and it is possible to make a highly accurate

charge calibration.

The radiation length of the electromagnetic part is about 20 X0 in the central

region and 30 X0 in the forward while it is about 5 interaction lengths λ in the central

and 8 λ in the forward area for the hadronic part.

The energy resolution for EM and HAD showers are:

σEME

E=

11%√

E[GeV ]⊕ 1%

σHADE

E=

50%√

E[GeV ]⊕ 2%

3.2.2.2 Spaghetti calorimeter (SPACAL)

The spaghetti calorimeter (SpaCal) consists of scintillating fibers embedded in a

lead absorber, parallel to the z-axis. As the LAr, the SpaCal also has electromagnetic

(EM) and hadronic (HAD) sections. The angular range covered is 155 < θ < 177.

The SpaCal has 1192 channels which are read out with a time resolution of 1 ns.


The molecules, excited by the particles passing through, emit scintillation light

which travels by the fibers to the photomultiplier tubes to be converted in electrical

signals. The SpaCal is used to measure the scattered electron at low Q2 and to

contribute to the reconstruction of hadronic final states.

The EM (HAD) corresponds to 27.8 X0 (2 λ). The EM and HAD energy resolu-

tion are:

σEME

E=

7%√

E[GeV ]⊕ 1%

σHADE

E=

56%√

E[GeV ]⊕ 7%

3.2.3 Luminosity system

The H1 luminosity system [74] main task is the relative measurement of the

luminosity as seen by the main detector. The measurement is based in the Bethe-

Heitler [75] process, ep → epγ, determined by the electron tagger (ET), photon

detector (PD) and Cherenkov counter (VC) detectors located close to the beamline

but far away from the interaction point (ET at z =-33.4 m and PD at z =-102.9 m) to

cover the small angles of the electrons and photons traveling in the primary electron

beam direction. The VC detector and a Pb filter 2X0 protect the PD from the high

synchrotron radiation flux.

Figure 3.9: Detection of the Bethe-Heitler event (ep → epγ) by the electron tagger(ET), photon detector (PD) and Cherenkov counter (VC).

The ET (PD) detects the scattered electrons (the photons) at approx. 0 - 5

(0 - 0.45) mrad as shown in Figure 3.9. The event rate R′, corrected of background


(mainly from electrons bremsstrahlung), is used for the luminosity determination:

L =R′

σvis

, (3.3)

where σvis is the visible part of the Bethe-Heitler cross section (with acceptance and

trigger efficiency included).

3.2.4 Trigger system

The H1 trigger system has the function of separating out the ep events containing

interesting physics from the background sources in the total 10.4 MHz input rate,

while keeping a minimum dead-time.

This system is divided into four levels, called L1 - L4, to facilitate the making of

decision as more H1 detector components combines their information. The events

fulfilling all level requirements are written to tape for permanent storage. The final

rate for storage is limited to 10 Hz. See Figure 3.10.

The first trigger level L1 provides a decision for each bunch crossing. The full

system run deadtime free at 10.4 MHz and is phase locked to the RF signal of HERA.

The decision delay is 2.3 µs and must reduce the event rate to 1 kHz.

The L1 must provide a sophisticated identification of the characteristics of an

event. It widely uses the track origin information, that uniquely distinguishes ep

interactions from the beam gas background, and for the ep events, where the vertex

information may not be the best requirement, the hadronic final state topology. So,

at first level only the MWPC and LAr calorimeter data are correlated in such a way.

The L1 output are called trigger elements (TE) which are sent to the central

trigger control (CTC) to be combined with other subtriggers.

The intermediate levels L2 and L3 are called synchronous, because they operate

during primary dead time of the readout. They are based on the same information

prepared by the L1 trigger.

The level 2 decision is made evaluating a large number of subsystems signal

correlation in detail. Its time decision is only 20 µs but is able to reduce the event


L1

µ

L3L2 L4

s

farmprocessor

processorfarmlogic

circuit

neuronalnetwork

topolog.trigger

full eventreconst.

~100 msµ22 sµs2.3 ~100

detector1 kHz~10 MHz

data

clear pipelines & restart

L1

subdetector

trigger data

L2 reject L3 reject

pipelines pipelines

stop read−out continuedata pipelines

keep keep keepL2 L3

L4

L4reject

read−out

max

50 Hz

maxmax

Dead timefree

Deadtime asynchronous phase

keep

write

10 Hz

on

ta

pe

reje

ct

200 Hz

Figure 3.10: The H1 trigger system consisting in four levels (L1 - L4). The eventsfulfilling all level requirements are written to tape for permanent storage.

rate to 200 Hz. L2 consists of two independent systems, the neural net trigger

(NNT) and the topological trigger (TT) trained with ep and background events and

a geometry of the detector in the θ and φ space samples.

In parallel, a flexible third level has 100 µs to take a decision using software

algorithms running on a microprocessor. It can potentially refine the trigger giving

a 50 Hz rate event at the end. In case of a rejection, the readout operations are

aborted and the experiment is alive again after a few µs.

The L4 filter farm is an asynchronous software integrated into the central data

acquisition system. It is divided into several logical modules to make a quick deci-

sion of the events (100 ms). If the event passes the selection criteria, it is written

to POTs (production output tape), in a rate of approx. 5 Hz, together with the

detectors information and an online calculation of the trajectory, energy signature

and momentum of all particles of the event, which is used for an event classification.

A small fraction of about ∼ 1% of the rejected events is kept for monitoring

purposes.

Chapter 4

Selection of DIS events and K0

Scandidates

The selection of the DIS event sample requires several steps, which focus in

cleaning the sample by reducing the contamination of the events of interest. The first

selection is independent of the analyser, hence this stage is called online selection,

and consists in the action of the trigger as described in section 3.2.4. Next, the offline

selection is carried out by many steps as the analyser decides depending in the aim

of study or the cleanliness wished for.

In the first section of this chapter a clear description of the online selection can

be found. The offline part is also described in detailed in the following sections,

starting with the selection of events containing the information of the needed de-

tectors, the commonly called run sample selection. Then, general cuts and the DIS

event selection are presented, finishing with the K0S candidates reconstruction. As

it was already pointed out, the K0S travel some distance before decaying to π+π−,

in the corresponding section it is explained how the V 0 (the vertex of decaying) is

reconstructed and the K0S identified from their daughters signature.

Several control plots of the used variables are going to be presented with the

comparison to the Django and Rapgap models.

59

60 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES

4.1 Trigger

The online selection consists of the subtrigger elements only. The subtrigger

chosen for this work corresponds to the level L1, the so called S67, which is defined

as:

S67 ≡ LAr && T0 && V ET

where LAr means the condition of the LAr calorimeter, T0 the timing condition,

VET the veto condition and the symbol && meaning the logical condition ’AND’.

99.9542 99.7864 95.217 99.9484 99.9565 100 99.6829 99.88 99.9678 96.5123 100 99.8834 100 99.7713 99.8298 99.976999.9877 99.9233 93.8361 99.9137 99.9442 99.871 99.901 99.9365 99.9519 99.9129 99.8842 99.9279 99.8989 99.9847 99.7917 99.979299.8758 99.9155 99.8903 99.8989 99.9411 99.9647 99.8834 99.7892 99.6705 98.961 98.2197 99.8992 99.8189 90.4458 98.9704 99.956199.9177 99.9069 97.3444 99.9366 99.982 99.9632 99.9745 99.9528 97.6126 99.9832 96.1395 99.8892 99.9571 97.7898 96.8944 99.988399.8932 99.9855 99.8168 96.8607 99.9526 99.9118 99.9664 99.9946 99.9736 99.9761 99.949 98.467 99.9369 99.9507 96.1926 99.944299.9563 99.9894 99.8406 99.97 100 99.9279 99.9522 99.9653 99.9386 99.8617 99.9626 99.974 98.7527 99.9681 94.5946 99.896199.9655 99.9393 99.5625 99.9399 99.9473 99.8996 97.2664 99.9141 98.8621 99.7811 99.8864 99.9666 96.4055 99.8805 97.4561 99.804699.9059 99.8264 99.1855 99.902 99.9299 99.9291 100 99.9656 79.8381 99.8441 99.5997 99.9857 98.0585 99.916 99.7256 98.711399.8913 99.9252 98.1199 99.9108 99.9373 99.9737 100 99.9564 97.5504 99.83 99.6129 99.9328 97.7725 99.9368 98.5646 95.796299.9195 99.984 99.9661 99.9755 99.9525 99.9356 93.8665 99.9742 99.9005 99.9797 99.9125 99.9129 83.0226 99.8959 81.333 77.714399.9675 99.9213 99.9705 99.9383 99.9875 99.9195 100 99.7448 99.9003 99.9705 99.8874 99.9005 68.7215 100 84.065 33.416899.8213 99.9052 99.9827 99.879 99.9839 99.9168 98.8292 98.6421 99.7893 99.8576 99.6564 99.9082 77.7557 99.9613 83.0409 63.8415

100 99.97 99.8849 99.9238 99.2569 100 100 99.4709 99.8962 100 99.9301 99.676 97.1034 99.8838 81.7131 99.7726100 100 99.8456 99.8148 99.8577 99.9237 99.9575 100 100 99.9198 99.9308 99.7838 96.8182 99.8193 66.413 98.7281

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99.9669 99.9913 99.9501 99.9715 99.9842 99.9877 98.8074 99.9521 99.985 99.9478 99.9029 99.9749 71.212 99.9607 75.2484 61.065799.8967 98.431 96.737 99.5331 99.9306 99.979 97.8479 99.3929 99.9435 99.9655 99.7354 98.9536 73.8497 99.9042 71.0374 59.20497.7969 99.9771 83.0882 99.9254 99.6524 99.9642 99.9885 99.9007 99.9245 99.9532 99.4254 99.905 97.9597 99.9852 81.0034 99.70197.4758 99.9938 85.069 99.9157 99.9619 99.9742 99.9766 99.9689 99.9938 99.9881 99.9947 99.9654 97.9646 99.9234 68.1829 99.924799.3004 99.9535 89.3778 99.8824 99.9693 99.99 99.9644 99.9975 99.9615 99.9119 99.9242 100 96.4463 99.9625 70.5263 99.854981.6463 99.9772 96.5316 99.9551 99.9405 99.984 99.9826 99.9672 99.9453 99.9416 99.9904 99.9636 91.7891 99.9848 73.1838 99.964861.4834 99.9935 98.1744 100 99.854 100 100 99.9784 99.9752 99.9865 99.9542 99.9819 90.2311 99.9528 90.8829 10093.4474 99.9798 99.06 99.9451 99.9654 99.9314 99.9356 99.9703 99.9731 100 99.9288 99.9644 98.8063 99.9743 86.1021 92.963499.9855 100 100 99.9807 99.9613 99.9802 99.9598 99.937 100 100 100 100 99.7921 100 87.5676 86.5385

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100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 99.5671 100 100 96.3967 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 95.2381 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 97.2222 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

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EMinus06 Fiducial Volume CutsEMinus06 Fiducial Volume Cuts

99.9782 99.9786 99.9854 99.9935 99.9807 99.9714 99.9622 99.9924 99.9845 100 99.9867 99.994 99.9904 99.9931 99.9284 99.975299.9955 99.9931 99.991 99.9906 100 99.9784 99.9412 99.9946 99.9832 99.9889 99.9979 99.9963 99.9962 99.995 100 99.967299.931 99.9807 98.6527 99.9931 98.7205 99.9847 99.9485 99.918 99.744 99.7332 99.9849 99.9781 99.9791 94.9018 99.8322 99.9703

99.9835 99.9945 99.9835 99.9892 99.9592 99.9966 99.9973 99.9898 99.9912 99.9906 99.9921 99.9834 99.9903 98.6865 99.9871 99.991899.9942 99.9775 98.7433 99.9901 99.9928 99.9739 99.9924 99.9842 99.9918 99.9892 99.9986 99.9928 99.9878 99.9867 99.99 99.990999.9958 99.9796 99.9824 99.9746 99.9957 99.9837 99.9921 99.996 99.9891 99.9952 99.9958 99.9961 99.9948 99.9772 99.9821 99.992799.9882 99.9913 99.929 99.9219 99.9956 99.9947 98.1516 99.9942 99.4314 99.0741 99.8767 99.9892 99.7845 99.9849 99.9714 99.961999.9903 99.9802 99.8536 99.189 99.9946 99.9982 97.3529 99.9621 93.4035 99.9396 99.8022 99.9919 99.6762 99.9796 99.9183 99.985899.9488 99.9963 99.5141 99.9981 99.9859 99.9853 100 99.9741 97.1647 99.9506 99.6879 99.9839 98.8471 99.964 99.9882 99.9999.9678 99.9928 99.9654 99.9565 99.9926 99.9935 100 99.9928 99.9829 99.9863 99.9493 99.9978 76.7002 99.9888 82.6118 73.1786

100 99.9926 99.9785 99.966 99.9936 99.996 100 99.9648 99.9956 99.9819 99.9074 100 58.2329 99.9929 82.1026 62.253299.8789 99.9763 100 99.9844 99.9598 100 100 98.9197 99.9835 99.4383 99.3758 99.9522 77.4827 99.9756 76.4192 63.229898.2369 100 82.4654 98.8987 99.9274 100 100 99.8779 99.9942 99.9664 100 99.9482 98.432 99.9749 67.6367 99.9175

100 99.9843 58.7025 99.9595 99.9699 100 99.9762 99.9868 100 99.9724 99.9767 99.5003 99.0731 99.9838 70.5262 99.758396.0687 100 85.0295 100 99.9858 100 100 99.9672 99.9131 99.9675 99.2159 99.2128 100 100 79.7101 99.878854.4085 99.9824 100 99.9646 99.9328 100 99.9698 100 99.9806 99.9904 99.9726 100 99.9794 99.9806 78.4 10032.4622 100 99.0823 99.984 100 99.977 99.9706 100 100 99.9713 100 100 100 100 65.407 10080.3377 99.9763 100 100 99.9388 100 100 100 99.9802 100 100 100 100 99.9519 93.6684 90.3061

100 100 100 100 100 99.9657 100 100 100 100 99.9692 100 99.7074 99.8462 100 98.1667100 100 100 100 100 100 100 100 100 100 99.6047 100 100 100 99.6094 98.0769100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 99.4898100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 97.7778 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 88.8889 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

)° (φ-150 -100 -50 0 50 100 150

(cm

)im

pZ

-200

-150

-100

-50

0

50

100

EPlus06 Fiducial Volume CutsEPlus06 Fiducial Volume Cuts

Figure 4.1: Trigger efficiency plots as functions of azimutal angle φ and z impactposition of the electron in the LAr calorimeter for 2004e+p, 0405e−p, 2006e−p and0607e+p periods. The enclosed areas correspond to the fidutial volume cuts negletedfrom the entire data (in red) and for some periods (in blue).

The LAr efficiency (εLAr) is measured with the events firing the S67 after removing

the subtrigger and fidutial volume cuts1. This can be determined thanks to the

1Cells switched off because high noise, damage or malfunctioning hardware.

4.2. DATA QUALITY CONSTRAINS 61

independence between the electron fired and the hadronic final states fired, so one

can be used to monitor the other one. The LAr efficiency becomes close to 100 % as

can be seen in the Figure 4.1 for the four periods (plots made by Maxime Gouzevitch),

where the efficiency value of each cell is depicted as function of φe angle and zimpact

position of the electron. The enclosed areas correspond to the fidutial volume cuts

(rejected cells) negleted from the entire data (in red) and for some periods (in blue).

The T0 efficiency εT0 is determined in a similar way as the εLAr using the inde-

pendent LAr calorimeter and the CIP2k detector as monitors. As it uses the LAr,

the fidutial cuts are also applied here. A 100 % efficiency is obtained.

The veto efficiency εveto is calculated by the contributions of the time of flight

(ToF), CIP2k and MUON detectors. It is found a εveto = 98.83 ± 0.42 for e− and

εveto = 99.13 ± 0.24 for e+.

When the AND condition is made, the efficiency εS67 is found to be ∼ 99 %.

For an extended explanation of the trigger efficiency determination see the sec-

tions 2.6, 2.7 and 6.2 of reference [76].

4.2 Data quality constrains

The first steps of the offline selection consists in the choice of the recorded events

containing all the data information needed for the study of this thesis. The run

sample selection also provides the luminosity value which is subsequently used in the

cross section determination.

The cuts belonging to the general event selection constrains are explain now and

listed in the first column of Table 4.2.

4.2.1 Run sample selection

The data recorded at the H1 tapes are separated in runs, which are basically

events occurring in a time interval and containing very similar operating detector

and accelerator conditions. They are classified as good, medium or poor depending


on the turn on subdetectors, the operating status and the quality of the lepton and

proton beams.

The run selection is a filter to obtain a sub-set of events where the detector

components relevant to this analysis are switched on and working properly. The

components required for K0S studies are CJC1, CJC2, CIP, LAR, SPACAL, TOF,

LUMI and VETO, with the additional condition of the trigger S67 and a primary

vertex range of ± 35.0 cm.

Table 4.1 lists the data periods considered here, the type of lepton, the run

ranges and the luminosity corresponding to the periods. It is important to remark

that not all runs of each year were used, some of them were rejected because of

detector malfunction, powerglitch, high voltage problem, noise or low yield, etcetera;

however the luminosity values presented are corrected for the rejected events. A total

luminosity of 339.6 pb−1 is obtained for the HERA II data.

Table 4.1: Run selection sample and corresponding luminosity value.

Year Collision Part. First Run Last Run L [pb−1]

2004 e+p 367284 392213 49.02

2004 e−p 398286 398679 0.160

2005 e−p 399629 436893 99.90

2006 e−p 444307 466997 56.87

2006 e+p 468531 492541 87.70

2007 e+p 492559 500611 45.92

Total 339.6

4.2.2 Vertex cuts

The ep collision should occur at the idealized primary interaction vertex (xvtx, yvtx,zvtx) =

(0, 0, 0), however there are technical difficulties to achieve this properly, specially at

the z axis, then a range of several centimeters around this nominal vertex should be

4.2. DATA QUALITY CONSTRAINS 63

considered. A typical range of |zvtx| < 35 cm is acceptable specially to reject contam-

ination of either the interactions of the particles from the beam with the residual gas

in the beampipe or the interactions between the electrons and the proton satellites2.

The distributions are shown in Figure 5.1 a) and Figure 5.4 a) for the DIS and the

K0S samples, respectively.

In addition, it is required that the vertex be central. This means that the vertex is

found by the central tracker chambers which provides high precision and reconstruc-

tion of the parameters compared with those reconstructed by the forward trackers.

4.2.3 DIS kinematic range

The kinematic variables referred here were already introduced in the subsec-

tion 1.1.1. The values of the photon virtuality Q2, inelasticity ye and x-Bjorken were

determined by the e method and eΣ method, as explained in appendix A, finding

at the end the same results within the systematic errors. The e method has been

chosen for the reconstruction of event kinematics in this work.

This analysis is focused at high Q2, meaning Q2 greater than 145 GeV2. This cut

ensures that the scattered electron is measured in the LAr calorimeter. An upper

cut, Q2 < 20000 GeV2, is also applied as precaution due to the limited phase space

at HERA. The Q2 distributions are shown in logarithm scale in Figure 5.1 b) for the

DIS sample and Figure 5.4 b) for the K0S sample.

The ye cut in the range 0.2 < ye < 0.6 is done to avoid the fake electrons and for

to be in a safety range of resolution of the e method, see Figures 5.1 c) and 5.4 c)

for the corresponding DIS and K0S sample distributions. There is not explicit cut

applied to x but due to its relation with the other kinematic variables it is affected,

see the distribution for DIS events in Figure 5.1 d).

2Small bunches delayed with respect to the main bunch.


4.3 Selection of DIS events

The next step consists in the DIS event selection, based on the identification of the

scattered electron e′. The criteria list in this case was chosen because high efficiency

of detection, resolution, geometrical acceptance of the detectors, physical rules of

conservation or because rejection of others kind of processes that are considered as

background in this analysis. The applied cuts have already been widely studied and

tested for other analysers and they are settle as the best for DIS events selection.

All these cuts are listed in the second column of the Table 4.2.

4.3.1 Scattered electron energy

According to the four-momentum Q2 of photon participating in the interactions

at HERA, e′ can be detected by the LAr or the SpaCal calorimeter. For this thesis,

the chosen phase space dictates that the electron must be identified by the LAr

Calorimeter.

The electron energy restriction is done to avoid the fake electrons (typically

hadronic clusters from photoproduction events) or the non well identified electrons,

but also to take advantage of the LAr efficiency which is close to 100% at E ′

e >11 GeV

(the distribution is presented in Figure 5.2 a)). The clear recognizion of the elec-

tron is possible because the position, shape and size of the cluster left by its energy

deposition in the LAr is very well known.

4.3.2 Scattered electron polar angle and zimpact coordinate

The limits on the polar angle θe and the impact coordinate in the z axis of the

electron zimpact are based on geometrical acceptance of the H1 LAr Cal detector.

The polar angle is defined as the angle between the incident proton beam direction

and the line given by the primary interaction vertex and the center of the energy

cluster in the LAr. The chosen range is 10 < θe < 150 (see its distribution in

Figure 5.2 b)).

4.4. RECONSTRUCTION OF K0S CANDIDATES 65

The z coordinate of the electron impact is chosen to be zimpact > −180 cm (Fig-

ure 5.2 c)) to ensure that the electron falls on the acceptance of the LAr calorimeter.

4.3.3 Four-momentum conservation

By conservation of energy and momentum, the value of the total E − pZ mea-

sured in H1 should be twice the energy of the incoming electron, that means 2∗27.5

GeV≃55 GeV, but several effects can affect this, for instance if the electron was not

detected in the LAr calorimeter, if there were initial or final state radiation so the

energy of the electrons is reduced or if photoproduction events occurred. Mainly due

to these possibilities the constrain 35 < E − pZ < 70 GeV is made, as shown in

Figure 5.1 e).

4.4 Reconstruction of K0S candidates

Once the DIS sample is available, one goes ahead with the particle identification

of interest, in this case the K0S meson. As the K0

S is a neutral particle, it only can be

detected through its daughter particles. As was listed in Table 2.2, this meson have

several decay channels but the one chosen for this analysis is the more frequent and

the one with only charged particles, K0S → π+π−; see Figure 4.6.

A general explanation of how to deal with the reconstruction of the K0S candidates

is the following:

1) Look for central tracks with opposite charge which satisfy the selection criteria

mentioned in section 4.4.1.

2) As the K0S has a relatively large lifetime it travels some distance before decay-

ing. The decay occurs at a vertex, displaced from the primary vertex, known as

secondary vertex V 0. The selected tracks in 1) are assumed to be the daughters

of a neutral particle and are associated to the V 0.


3) The last step consists in a series of cuts applied to the identified neutral particle

to decide if it can be considered as a candidate to K0S .

The summary of all the cuts applied to the tracks and the K0S candidate can be

found in the two last columns of the Table 4.2.

4.4.1 Track cuts

In H1, the tracks can be reconstructed by only central trackers, only forward

trackers or by the combination of both, but the best quality of reconstruction comes

from the central trackers. That is the reason why these are chosen here.

Reconstructed tracks with a starting radius less than 30 cm are chosen (see Fig-

ure 5.3 a)). This condition implies tracks whose beginning is located inside the CJC1

detector avoiding in this way the consideration of pieces of trajectories produced by

the interaction with the material between the CJC1 and CJC2.

A combination of the track segments of the CJC1 and CJC2 chambers provides

a better reconstructed track, then a cut to the length of the transverse projection of

the tracks is applied with the restriction of radial length > 10 cm to get a track of

good reconstruction quality, Figure 5.3 b).

It is known from previous studies that the reconstruction of the tracks get worse

at very low transverse momentum values because of the multiple interactions with

the material of the detector and the curling of the trajectory, therefore a cut of

pt > 0.12 GeV is applied to each track to have a good identification and to avoid

background of wrong tracks. The distribution is presented in Figure 5.3 c) for the

π− of the K0S.

The cut dca(π+)∗dca(π−) < 0, where dca means the distance of closest approach

to the origin of the interaction as explained in appendix D, is done to ensure that

a pair of selected opposite charged tracks share the same V 0; but also to test the

charge of the considered particles, because due to the magnetic field the tracks with

opposite charges should bend in different directions giving a negative value of their

dca product.


The so called significance |dca′|/σdca′ , the ratio of the absolute value of the dca′

(the distance of closest approach of the track in the rφ plane to the primary vertex)

and its error σdca′ is chosen to be greater than 3; this constrain helps to reject

tracks coming from the primary vertex. Studies made by D. Pitzl and A. Falkiewicks

showed that more statistic and better signal to background ratio is obtained with

the application of this cut complemented with the dca(π+) ∗ dca(π−) < 0 constrain.

The distribution of significance for the π− from the K0S can be seen in Figure 5.3 d).

Table 4.2: Summary of the selection criteria.

Event selection Electron cuts Tracks cuts K0S cuts

central vertex Trigger 67 Central tracks > 1 Number of K0S >0

|zvtx| <35 cm Ee > 11GeV Different charges Daughters = 2

145< Q2 < 20000GeV2 10 < θe <150 Start radius < 30cm Decay length >2cm

0.2< Ye <0.6 zimpact >-180cm Radial length > 10cm |η| <1.5

35< E − pz < 70GeV pt > 0.12GeV pt >0.3GeV

Fiducial cuts dca(π+) ∗ dca(π−) <0 M(pπ−) >1.125GeV

|dca′|/σdca′ >3 M(e−e+) >0.05GeV

Fit χ2 <5.4

| cos(θ⋆)| < 0.95

4.4.2 Cuts to the K0S candidates

Until here, the selection criteria provides the two candidates to πs tracks and the

V 0 position. If the number of found V 0’s is different of zero. Then, one can follow

with the next conditions.

The phase space of this analysis is characterized by the Q2 and ye kinematic

ranges but also by the transfer momentum pt(K0S) and the pseudorapidity |η(K0

S)|limits of the K0

S :

0.3 GeV < pt(K0S) |η(K0

S)| < 1.5


The pt(K0S) cut is chosen to have good acceptance and good efficiency on the

reconstruction of the V 0 from the pions tracks, while the η(K0S) cut is used to ensure

that the K0S is contained within the geometrical acceptance of the central detectors.

Positive (negative) values of η corresponds to the forward (backward) region of the

H1 detector, so it can be traduced to θ cuts, see Figure 5.4 d) and e).

The distance in the rφ plane between the primary vertex and the secondary vertex

V 0, known as the radial decay length, is chosen to be DL > 2 cm (Figure 5.4 f)),

mainly due to the efficiency of V 0 reconstruction and the boost of the K0S lifetime to

the laboratory frame.

Another cut applied to the vertex finding is the χ2 quantity which expresses the

quality of the fit of the two daughter particles to the secondary vertex. A value of

χ2 < 5.4 is considered as good enough since the distribution decays exponentially

and start to be almost flat from approx. χ2 = 3, as shown in Figure 5.5 a). A value

of 5.4 allows to have a little bit more statistic.

The angle between the positive track in the rest frame of the K0S and the direc-

tion of the K0S in the laboratory frame is the so called θ∗ angle. A requirement of

|cos θ∗| < 0.95 is applied to the selection in order to avoid background from photon

conversion (γ → e+e−) and ensure that the K0S candidate comes from the primary

vertex. Figure 5.5 b) shows the distribution of this variable.

The way to improve the rejection of neutral particles faking the K0S reconstruc-

tion, for instance the photon conversion, Λ0 and Λ0 particles, between others, is

calculating the invariant mass and making some cuts to it.

The invariant mass M can be calculated under the hypothesis of the π mass for

both negative and positive tracks3 by the formula:

M(π+, π−) =√

(Eπ+ + Eπ−)2 − (pπ+ + pπ−)2 (4.1)

where pπi is the momentum vector, Eπi =√

p2πi + m2

π the energy, mπ the pion

mass [11] of the pion i = + or i = −.

3From the track reconstruction is possible to extract the momentum vector but not the mass ofthe particle. The four-momentum can only be obtained by assuming a mass value.


d

V0

pprel

1 d2

p1,L

2,L

prel

TT

K0s π

Λ p πΛ p π_ _

0 10.69

+

PT

rel [GeV]

α−1

0.104

0.206

+ −

π−

−0.69

Figure 4.2: a) Definition of longitudinal pL and the relative transverse prelT momentum

variables. b) The armenteros plot where half ellipses with its center lying at α axisbelong to V 0 particles. The value of the centers gives the difference between themasses of the daughters.

a) b)

The Λ0 and Λ0 contributions are eliminated by requiring M(pπ) > 1.125 GeV,

assuming the π− and p masses for the invariant mass calculation when the search is

for Λ0, or the π+ and p masses for Λ0 [11]. The track with the highest momentum is

considered to be the p or p according to the charge of the track.

In the same way, the photon conversion contribution is avoided by M(e+e−) >

0.05 GeV. The masses considered here are those of the electron e− and positron

e+ [11].

The values of the last two cuts were obtained using the Armenteros-Podolsk-

Thompson plots [77], which plot the α vs. prelT variables to describe the kinematic of

a body decaying to two daughters d1 and d2. α is defined as:

α =pd1

L − pd2

L

pd1

L + pd2

L

where pdi

L is the longitudinal momentum measured in the laboratory frame of the

daughters with respect to the flight direction of the mother particle; prelT is the

value of the relative transverse momentum of the daughters, see Figure 4.2 a). The

condition prelT (d1) = prel

T (d2) is imposed by momentum conservation.


Figure 4.3: Armenteros plots from all HERA II data.

) [GeV]-π +πM (0.3 0.4 0.5 0.6 0.7

Ent

ries

/ 3 M

eV

0

1000

2000

3000

4000

5000

-π +π → s0K

1194±) = 38154 s0 N(K

H1 Preliminary

Figure 4.4: Invariant mass distribution of the K0S candidates reconstructed from the

decay channel π+π−. The corresponding fits to describe signal and background areshown in red and blue lines respectively, while the total fit is plotted with the greenline.


A typical Armenteros plot is shown in Figure 4.2 b) where half ellipses with

its center lying on α axis belong to V 0 particles. The value of the centers gives

the difference between the masses of the daughters. The band structure is due

to momentum conservation of the different V 0 decays, while the band widths are

determined by the widths of the V 0s combined with the detector resolution. The

bands of Λ0 and Λ0 are lower than the K0S band. The reason is that the sum of the

pion and proton masses is only 38 MeV smaller than the Λ0 mass, while the sum

of the two pions is ∼219 MeV below the K0S mass. Due to the finite resolution the

measured distributions are smeared out. However, the separation of K0S and Λ0 still

can be seen. In Figure 4.3, the Armenteros plot from HERA II data is presented,

the rejection of Λ0 particles has already be done.

) [GeV]-π +πMass(0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

En

trie

s/

1 M

eV

-210

-110

1

10

210

310

Decays0K DecayΛ

Other Decay Pair Prod→ γ

Secundary Inter.Other vertex

Django HERA II

comes from:-π +π

) [GeV]-π +πMass(0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

En

trie

s/

1 M

eV

-210

-110

1

10

210

310

Decays0K DecayΛ

Other Decay Pair Prod→ γ

Secundary Inter.Other vertex

Rapgap HERA II

comes from:-π +π

Figure 4.5: Invariant mass distribution of the K0S for Django and Rapgap models.

The study of the remaining contamination shows some contribution of Λ decays,other particles decaying to two charged daughters, photon conversion, interactionswith the dead material of the detector and events coming from other vertex.

After applying all mentioned cuts, the mass distribution of the K0S candidates is

plotted and shown in Figure 4.4. A clear peak is obtained concluding that most of

the background has been rejected. However, using Monte Carlo models, a study of


the remaining contamination can be done showing that still some few events of Λ

decays, other particles decaying to two charged daughters, photon conversion (γ →pair production), secondary interactions (interactions with the dead material of the

detector) and events coming from other vertex are part of the sample, in Figure 4.5

Django and Rapgap models results are presented, similar predictions are obtained.

Figure 4.6: Seagull and sailor decay topologies identified by the sign of the crossproduct of the three-momentum of the pions, (~pπ+ x ~pπ−)z > 0 for seagull and(~pπ+ x ~pπ−)z < 0 for sailor.

a) b)

The invariant mass distribution shown in Figure 4.4 contains in fact two different

track combinations of curvatures or decay topologies, the outward-curved or seagull

and the inward-curve or sailor topologies both depicted in Figure 4.6. The separation

of these can be done by the cross product of the three-momentum of the pions, the

seagull decay topology is defined as (~pπ+ x ~pπ−)z > 0, whereas the sailor decay

topology corresponds to (~pπ+ x ~pπ−)z < 0. The K0S mass distributions for each

topology are presented in Figure 4.7.

4.5 Event yield

The event yield Y is defined as the ratio of the number of events in the sample

(N) and the integrated luminosity as measured in section 3.2.3, corresponding to the

4.6. SIGNAL EXTRACTION 73

-) [GeV]π +πM (0.3 0.4 0.5 0.6 0.7

Ent

ries

/ 3 M

eV

0

200

400

600

800

1000

1200

1400

1600

1800

2000 -π +π → s0K

0.000122±Mass = 0.497388

0.000146± = 0.010593σ

723±) = 18285 s0 N(K

S/B = 5.610861

Seagull

) [GeV]-π +πM (0.3 0.4 0.5 0.6 0.7

Ent

ries

/ 3 M

eV

0

500

1000

1500

2000

2500

-π +π → s0K

0.000088±Mass = 0.496719

0.000113± = 0.007467σ

936±) = 20042 s0 N(K

S/B = 3.946869

Sailor

Figure 4.7: Invariant mass distribution of the seagull and sailor topologies showing9% higher contribution from sailor compared with seagull.

a) b)

selected run period, then Y = N/L.

An abnormal low or high yield may indicate a period where the detector efficiency

or measured integrated luminosity is not well understood. In Figure 4.8 the yield

plots as a function of the run number, also separated by year periods, are presented

for the DIS sample and K0S sample, respectively. It is in general stable. The small

changes have been observed in other analysis and have been attributed to biases in

the integrated luminosity measurement (acceptance of the photon tagger).

4.6 Signal extraction

To know the number of K0S candidates is necessary to make a fit to the invariant

mass distribution. Figure 4.4 shows the total fit ftot(mπ+,π−) as a green line, which is

in fact a sum of two functions, one to describe the signal fsig(mπ+,π−) showed with a

red line in the Figure and one describing the background fbgrd(mπ+,π−) in blue line:

ftot(mπ+,π−) = fsig(mπ+,π−) + fbgrd(mπ+,π−).

The function chosen for the signal is the t-student distribution:

fsig(xm(π+,π−)) =N Γ((ν + 1)/2)√

νπ Γ(ν/2)(1 +

t2

ν)−(ν+1)/2,


Run Number380 400 420 440 460 480 500

310×

Yie

ld (

Eve

nts/

1 pb

)

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4 +Data 04 e-Data 0405 e

-Data 06 e+Data 06 e+Data 07 e

DIS sample

Run Number380 400 420 440 460 480 500

310×

Yie

ld (

Eve

nts/

1 pb

)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35+Data 04 e

-Data 0405 e-Data 06 e+Data 06 e+Data 07 e

Candidatess0K

Figure 4.8: Yield plots as a function of run number for a) the DIS sample and b) theK0

S sample. The 2004e+p period in blue, 0405e−p in magenta, 2006e−p in yellow,2006e+p in green and 2007e+p period in red.

a)

b)

4.6. SIGNAL EXTRACTION 75

t =xm(π+,π−) − µK0

s

σ,

where the normalization N , the mean value of the mass µK0s, the standard deviation

σ and the number of degrees of freedom ν are free parameters. The variable xm(π+,π−)

runs over the complete x axis range of the invariant mass distribution.

The t-student, as many other functions, is very useful to estimate population

values from the data samples, specially when the media and standard deviation are

not known. Some advantages are its continuity and symmetry with respect to the

average but one should pay special attention to the parameters and the χ2 values to

be sure that the fit is valid. In this case for instance, one should look at ν > 1, µK0s

close to the value provided by PDG [11], small σ and χ2 normalized to the degrees

of freedom (NDF) as close to 1 as can be possible.

This function was also chosen because of its bell shape a little bit lower and wider

than the normal standard distribution; as well due to its approximation to the Breit-

Wigner function when ν = 1; also because if ν has a high value (approx. ν > 200)

the distribution is more like a normal standard distribution; and because it behaves

as Gaussian when ν → ∞.

The best function for the background was found to be:

fbgrd(xm(π+,π−)) = p0(xm − 0.344)p1 ∗ Exp(p2xm + p3x2m + p4x

3m)

where pi are the free parameters. This choice gives a good description of the back-

ground shape which goes to zero at the value 0.344 GeV, due to a cut in the relative

transverse momentum of the pion (prelT ) of 100 MeV which traslates to a minimum

mass of 2√

m2 + (0.10)2 = 0.344.

The number of K0S candidates are taken from the integral of the signal func-

tion. The fit to the invariant K0S mass for all HERA II data, Figure 4.4, gives

38154 ± 1194 K0S candidates with a estimated mass in the peak of 496.97 MeV and

low σ (8.85x10−3). The ratio signal over background S/B in the range [0.45 GeV,

0.55 GeV] is 4.5.


4.7 Selection of charged particles

The charged particles (h±) sample is needed for the determination of the K0s /h

±

cross section ratio. They are selected in the same phase space as the K0S, 145 < Q2 <

20000 GeV2 and 0.2 < y < 0.6, together with additional conditions to ensure the

good quality of the tracks.

The tracks are detected by the CTD specially by the CJC chambers. The char-

acteristics to fulfill are:

• The track of the scattered electron is not considered in the sample.

• The cosine of the angles between the momemtum of the scattered electron and

the track of the charged particle must be less than 0.99 to reject tracks close

to the scattered electron.

• All tracks must be associated to the primary vertex such that the distance of

closest approach of the track in the rφ plane to the primary vertex is chosen

to be |dca′| < 2.0 cm.

• The minimum radial length of the reconstructed track must be greater than 10

cm.

• The tracks must have the first hit in the CJC1, then the start radius is chosen

to be less than 30 cm.

• The tranverse momentum required to be larger than pT > 0.3 GeV for good

efficiency of the track reconstruction and compatibility with the phase space

of the K0S sample.

• The psedorapidity range being between -1.5 < η < 1.5 as the K0S sample which

means that the tracks are in the central region of the detector.

After the selection a sample consisting of 2,615,100 charged particles is obtained,

mainly populated by charged pions.

Chapter 5

The measurement of the crosssection

As mentioned previously, the goal of this thesis is the measurement of the K0S

particle production. In this chapter is explained how the total production cross

section is determined and the way to calculate differential cross section as a function

of one or more variables; also a series of important issues of data correction that one

should not forget to take into account during the calculations.

The measurement from data is never an exact value. It is always accompanied of

additional quantities which represents the statistical and the systematic uncertain-

ties; this last one consisting on several sources which are explained in the last part

of this chapter.

5.1 Determination of the cross section

The interaction between two particles is generally described in terms of the cross

section. This quantity essentially gives a measure of the probability for a reaction to

occur and may be calculated if the form of the basic interaction between the particles

is known.

Two methods are commonly used to directly measure total cross sections. The

77

78 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION

first method is the transmission experiment where one measures the intensity of

particles before and after the target and infers the total cross section from the relation

I = I0exp(−NσT ), where I(I0) is the transmitted (incident) intensity and N is the

number of target nuclei per cm2. This method is frequently employed at fixed target

accelerators. In the second method one attempts to record every interaction that

takes place, this requires a detector with ∼ 4π acceptance. This method is often

used for colliding beam experiments, like at HERA. The total cross section is given

by σT = N/L where N is the measured total interaction rate and L is the measured

incident luminosity.

The total K0S cross section in the visible phase space defined by:

145 < Q2 < 20000 GeV2, 0.2 < ye < 0.6,

−1.5 < η(K0s ) < 1.5, 0.3 GeV < pT (K0

s ), (5.1)

is measured using the relation:

σvis(ep → e′K0s X) =

NdataK0

s

ε · BR(K0s → π+π−) · L (5.2)

where NdataK0

sis the number of K0

S mesons gotten from the fit to the invariant mass

distribution of data, as described in the section 4.6; ε the efficiency of detection with

the QED corrections included; BR the branching ratio of the K0S decaying to two

pions and L the accumulated luminosity.

The differential cross section in terms of a variable ℘ is calculated by:

dσvis(ep → e′K0s X)

d℘=

NdataK0

s

∆℘ · ε · BR(K0s → π+π−) · L (5.3)

where ∆℘ will take values of the different intervals of ℘, the so called bins. NdataK0

s

and ε should be now calculated for each bin. The values for NdataK0

swere obtained

after fitting the mass distribution for each bin, as shown from Figure F.1 to F.16

in appendix G for the bins of laboratory and Breit frame1 variables refered in the

1Description of the Breit frame in the appendix E.

5.1. DETERMINATION OF THE CROSS SECTION 79

Table 5.1. The same will be applied when double differential cross section as a

function of ℘ and 0 are required, the values needed for the measurement of the cross

sections should correspond to those bins of ∆℘ and ∆0.

5.1.1 Binning scheme

For the calculation of the differential cross section of the K0S belonging to the

final sample, one must split in different intervals the variable range. The size of the

intervals, known as bins, are chosen depending on the statistical data sample as fine

as one could, but ensuring that they are wide enough to get a good fit to the invariant

mass distribution of each bin, so it can occur that some bins are larger that others.

The bin width is also checked to be at least twice its resolution. A good binning

choice can help to limit the statistical error on the differential cross section.

Here, the data sample was binned as a function of the kinematic variables Q2, x

and the K0S variables η and pt in laboratory frame and also as a function of xCBF

p ,

xTBFp , pCBF

T and pTBFT in the Breit frame using the bin boundaries listed in Table 5.1

and bounded by the corresponding phase space cuts.

Table 5.1: The bin boundaries list.Q2[GeV 2] x η PT [GeV] XCBF

p XTBFp PBF

t [GeV ]

145,167 0.0,0.004 -1.5,-0.5 0.3,0.8 0.0,0.07 0.0,0.07 0.0,0.35

167,200 0.004,0.008 -0.5, 0.0 0.8,1.1 0.07,0.13 0.07,0.13 0.35,0.6

200,280 0.008,0.017 0.0, 0.45 1.1,1.55 0.13,0.2 0.13,0.2 0.6,1.0

280,500 0.017,0.2 0.45, 0.95 1.55,2.23 0.2,0.33 0.2,0.33 1.0,1.8

500,1000 0.95, 1.5 2.23,3.5 0.33,1.0 0.33,1.0 1.8,14

1000,5000 3.5,14 1.0,2.0

However, the binning used for the differential cross section is acceptable only if it

also satisfies other detector requirements (the efficiency ε, stability S, purity P and

acceptance A) as described in the following section.


5.2 The correction of data

For the cross section extraction, the data is submitted to corrections because of

loses of the K0S from the sample or the inclusion of fake K0

S in the sample, both

possibilities can occur due to the incapability of the detectors to capture all the

particles produced (geometrical and electronic acceptance), the limitations in the

track reconstruction due to the selection criteria, fluctuations in the physical variables

determination due to finite resolution, the possible rejection of particles of our interest

during the signal extraction, etc.

The corrections are done using Monte Carlo simulations. There are three different

kinds of MCs mentioned in section 1.4, the generated MCs and the reconstructed

MC. The generated are the radiative MC and the non-radiative MC, based in the

simulations of the HERA collision. The first one takes into account QED radiative

effects. The reconstructed MC has the consideration not only of the HERA collider

but also the H1 detector conditions of operation. The reconstructed particles pass

by the same selection criteria and cross section extraction as data.

5.2.1 Control plots

A comparison between the data and the reconstructed Monte Carlo is done for

the complete event sample. The kinematic, DIS, tracks, K0S and other detector vari-

ables are compared in order to know the quantitative agreement between the data

and simulation. Those plots, called control plots, were done and checked for each

year period, as well for all HERA II data sample as shown in Figures 5.1, 5.3 and 5.4

where the data are compared to the Django and Rapgap models with normalization

to the number of events. It can be concluded that the simulations of the two models

describe reasonably well the distribution of several variables from data (the back-

ground as well). Then, the detector response to expected physics is well understood

and represented by efficiency reweights and detector simulation.

5.2

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[cm]vtxZ-40 -30 -20 -10 0 10 20 30 40

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trie

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2000

4000

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24000HERAII DataDjangoRapgap

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2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

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HERAII DataDjangoRapgap

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Figu

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Con

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eK

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ple,

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Figu

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Con

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610

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HeraII DataDjangoRapgap

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1

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210

310

410

510

610 b)

Track multiplicity0 5 10 15 20 25 30 35 40

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150

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Figu

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Con

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san

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Djan

goan

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Mon

teC

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ectively.

5.2. THE CORRECTION OF DATA 87

5.2.2 Reweighting procedure

As mentioned in the previous subsection and also to have reliability of the gener-

ated Monte Carlo data to be used further on, it is important that the Monte Carlo

models describes well the data distributions. Sometimes the first comparison shows

that the MC does not agree with data, in that case (if the differences are not too

large) a satisfactory description can be achieved by applying a reweighting procedure

to the MC.

One takes a measured distribution in data and the corresponding in Monte Carlo

to determine the event weight. In this thesis a reweighting of the observable (E −pz)HFS of the hadronic final states was done. The first step is to get the ratio of the

MC over the data distribution, secondly the event weight is calculated fitting the

ratio to a function F((E − pz)HFS) of an appropriate shape. The fit function used

here is the polynomio:

F(§) = p0 + p1x + p2x2.

The procedure is done for each year period independently, so the weights are not

the same. Besides an improvement of the data description by MC in the reweighted

distributions, which is of course expected, other distributions are also positively

affected. A spoiling of the description of other distributions has not been observed.

There are cases where the MC reweighting of one observable is not enough, then

the procedure can be done using another observables and, under the assumption

that these quantities are uncorrelated, the total event weight is given by the product

of single weights Wtot(obs1, obs2, obs3) = W (obs1)W (obs2)W (obs3). This assumption

seems to be approximately correct, since usually already after the first iteration a

quite reasonable data description is achieved.

Altogether with (E − pz)HFS reweighted other default H1 weights are applied in

this analysis: zvtx, trigger and PDF. Whereas the first two are related to the detector

simulation, the remaining is directly sensitive to the physics implemented in the MC

model.


5.2.3 Purity and Stability

Other detector effects can be studied using both reconstructed and generated MC

simulations, as the migrations effects (the purity P , stability S and resolution σres)

described in this subsection, which corrects the reconstruction or generation of events

in wrong bins. The migrations effects are quantifed by the purity P and stability S;

which can be defined as the ratio of K0S generated and reconstructed in a given bin

over the K0S reconstructed for P (generated for S) in the same bin, respectively:

P =N stay

i

N reci

, S =N stay

i

N geni − N lost

i

,

where the following combinations were taken into account:

• N stayi : the number of events reconstructed (passing the selection) and generated

in the same given bin i, Figure 5.7 a).

• N smear−outi : the number of events generated in the given bin i but reconstructed

in the bin j. Figure 5.7 b).

• N smear−ini : the number of events reconstructed in the bin i but generated from

the bin j. Figure 5.7 c).

• N losti : the number of events generated in the given bin i but do not recon-

structed because did not pass the selection. Figure 5.7 d).

• N reci = N stay

i + N smear−ini , the number of events reconstructed in the bin i.

• N geni = N stay

i + N smear−outi + N lost

i , the number of events generated in the bin

i.

As their name indicates, they say how much pure and stable the K0S sample

is. The unity is never completely reached, nevertheless is expected that the large

fraction of events belongs to the bin where they are measured in. For this thesis the

purity and stability values calculated for Q2, x, η(K0s ) and pT (K0

s ) are presented in


a) Stay

c) Smear−in d) Lost

b) Smear−out

i jout

Rec

Gen

i jout

Rec

Gen

i jout

Rec

Gen

i jout

Rec

Gen

Figure 5.7: Schematic view of migrations possibilities: stay, smear-out, smear-in andlost.

a) b)

c) d)


Figure 5.8 in the laboratory frame, while the corresponding plots for xBFp and pBF

T in

the current and the target hemispheres of the Breit frame are shown in Figure 5.9.

The Figures correspond to Django MC; Rapgap gives similar values as shown in

Table 5.2 for bins of x.

Table 5.2: Purity and Stability values in bins of x estimated from Django and Rapgapmodels.

Purity Stability

Django Rapgap Django Rapgap

x - Bin 1 86.95 86.62 82.37 82.56

x - Bin 2 88.32 88.13 87.67 87.74

x - Bin 3 86.21 86.47 87.94 87.80

x - Bin 4 91.49 91.92 94.08 94.20

The purity and stability are greater than 80% as functions of Q2, x and η(K0s ). A

rise is observed as Q2 goes higher, the same can be said for x, while η(K0s ) is almost

flat from the second bin. The purity as function of pt(K0s ) improves a little bit from

∼ 74% to around 82%, then decreases again but not less than 70%; the stability, on

the contrary, starts around 80% then decreases to 76%, at high pT bins the values

incresases until ∼83%. In the Breit frame, the purity and stability as function of

xBFp are around 80% for both regions, although flatter for the current hemisphere;

however as function of pBFT the values oscilate between 60% to 80%.

5.2.4 Efficiencies

The efficiency of reconstruction ε appearing in the equation 5.2 and 5.3 is in fact

a combination of two efficiencies ε = εnon−raddet · εtrigger, the non-radiative detector

efficiency εnon−raddet and the trigger efficiency εtrigger. However the efficiency of the S67

trigger used in this analysis at high Q2 as explained in section 4.1 is ∼100%, so it is

taken as 100% and an error of 1% is included in the systematic uncertainties, then


[GeV]2Q310

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Purity

StabilityHERA II

Candidatess0K

X-310 -210 -110

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Purity

Stability

HERA II Candidatess

0K

η-1.5 -1 -0.5 0 0.5 1 1.50.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Purity

Stability

HERA II Candidatess

0K

[GeV]TP1 10

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Purity

Stability

HERA II Candidatess

0K

Figure 5.8: The K0S purity (in black) and stability (in green) as a function of Q2, x,

η and pT in the laboratory frame.

CurrentpX

-210 -110 10

0.2

0.4

0.6

0.8

1

1.2

Purity

Stability

HERA II Breit Frames

0K

TargetpX

-210 -110 10

0.2

0.4

0.6

0.8

1

1.2

Purity

Stability


0K

[GeV]CurrentTP

-110 1 100

0.2

0.4

0.6

0.8

1

1.2

Purity

Stability


0K

[GeV]TargetTP

-110 1 100

0.2

0.4

0.6

0.8

1

1.2

Purity

Stability


0K

Figure 5.9: The K0S purity (in black) and stability (in green) as a function of xp and

pT in the current and the target hemispheres of the Breit frame.


the efficiency becomes ε = εnon−raddet . The εnon−rad

det is defined as the ratio between the

number of K0S taken from the signal extraction of the reconstructed Monte Carlo

sample and the number of K0S from the generated MC, both in the same phase space

and satisfying the complete selection criteria listed in Table 4.2:

εnon−raddet = εrad

det ∗ (1 + δQED) =N rec(K0

s )

N genrad (K0

s )∗ (1 + δQED), (5.4)

here N genrad (K0

s ) indicates that this number was taken from the MCs including QED

initial and final state radiation, then could be that wrongly reconstructed (falling in

a different bin) K0S exists due to the change in the four-momentum of the scattered

electron. The way to correct for these QED events is introducing in QED correction

factor (1 + δQED) defined as:

1 + δQED =N rad

gen

Nnon−radgen

· Lnon−rad

Lrad, (5.5)

where, Lnon−rad and Lrad denotes the luminosity of the generated radiative and non-

radiative samples.

The QED corrections for bins of Q2, x, η(K0S) and pT (K0

S) in the laboratory

frame are shown in Figure 5.10 for K0S and 5.11 for charged particles using Django

and Rapgap models, the QED correction average is found around 5.5% with a flat

behaviour in terms of Q2, x and pT (K0S) while η(K0

S) presents a QED correction

increasing in the forward direction.

The plots of QED corrections for K0S in the Breit frame variables are shown in

Figure 5.12, the xCBFp and pCBF

T in the current region presents lower QED corrections

compared to the same variables in the target region. At high values of both variables

(xp and pT ) at target region a difference in the models corrections is observed.

The plots of the efficiency of reconstruction εnon−raddet are shown in Figures 5.13,

5.14 and 5.15 for the same variables as QED corrections, the average efficiency used

for the total inclusive cross section determination is ∼ 30.55 % but it varies from

bin to bin. As functions of x and η it behaves very stable but for Q2 and pT (K0S)

goes from ∼ 20% in the first bins to around 40% (a little bit higher for pT ) in their


]2 [GeV2Q310

Gen

Rad

/Gen

Non

Rad

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4Django CDM

Rapgap MEPS

X-310 -210 -110

Gen

Rad

/Gen

Non

Rad

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4Django CDM

Rapgap MEPS

η-1.5 -1 -0.5 0 0.5 1 1.5

Gen

Rad

/Gen

Non

Rad

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4Django CDM

Rapgap MEPS

[GeV]TP1 10

Gen

Rad

/Gen

Non

Rad

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4Django CDM

Rapgap MEPS

Figure 5.10: QED corrections of K0S as a function of Q2, x, η and pT in the laboratory

frame. The Django MC presented in red and the Rapgap MC in blue.

]2 [GeV2Q310

Gen

Rad

/Gen

Non

Rad

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Django CDM

Rapgap MEPS

X-310 -210 -110

Gen

Rad

/Gen

Non

Rad

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Django CDM

Rapgap MEPS

η-1.5 -1 -0.5 0 0.5 1 1.5

Gen

Rad

/Gen

Non

Rad

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Django CDM

Rapgap MEPS

[GeV]T

p1 10

Gen

Rad

/Gen

Non

Rad

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Django CDM

Rapgap MEPS

Figure 5.11: QED corrections of charged particles as a function of Q2, x, η and pT

in the laboratory frame. The Django MC presented in red and the Rapgap MC inblue.


CBFpX

0 0.2 0.4 0.6 0.8 1

Gen

Rad

/Gen

Non

Rad

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4Django CDM

Rapgap MEPS

TBFpX

0 0.5 1 1.5 2

Gen

Rad

/Gen

Non

Rad

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Django CDM

Rapgap MEPS

[GeV]CBFTP

-110 1 10

Gen

Rad

/Gen

Non

Rad

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4Django CDM

Rapgap MEPS

[GeV]TBFTP

-110 1 10

Gen

Rad

/Gen

Non

Rad

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Django CDM

Rapgap MEPS

Figure 5.12: QED corrections of K0S as a function of xp and pT in the current and

the target hemispheres of the Breit frame. The Django MC presented in red and theRapgap MC in blue.

]2 [GeV2Q

310

ε

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Django CDM

Rapgap MEPS

X-310 -210 -110

ε

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Django CDM

Rapgap MEPS

η-1.5 -1 -0.5 0 0.5 1 1.5

ε

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Django CDM

Rapgap MEPS

[GeV]TP1 10

ε

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Django CDM

Rapgap MEPS

Figure 5.13: Efficiencies of K0S as a function of Q2, x, η and pT in the laboratory

frame. The Django MC presented in red and the Rapgap MC in blue.

5.3. THE SYSTEMATIC UNCERTAINTIES 95

middle range, going down again to around 32% at the highest bins. This shows an

up and down behavior which is also observed in the Breit frame variables where the

difference in the models at high values in the target regions still remains.

]2 [GeV2Q310

Cha

rged

Par

t.ε

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3Django CDM

Rapgap MEPS

x-310 -210 -110

Cha

rged

Par

t.ε

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3Django CDM

Rapgap MEPS

η-1.5 -1 -0.5 0 0.5 1 1.5

Cha

rged

Par

t.ε

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Django CDM

Rapgap MEPS

[GeV]T

p1 10

Cha

rged

Par

t.ε

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3Django CDM

Rapgap MEPS

Figure 5.14: Efficiencies of charged particles as functions of Q2, x, η and pT in thelaboratory frame. The Django MC presented in red and the Rapgap MC in blue.

5.2.5 Resolution

The resolution of a variable X is defined as the width of the distribution:

σres = Xrec − Xgen

where Xrec and Xgen denotes the reconstructed and the generated value of the variable

X, respectively. The resolutions are shown in Figures 5.16 and 5.17.

5.3 The systematic uncertainties

The accuracy of the cross section measurement is altered by several sources of

uncertainty which change the determined value by a ∆σ. The study of these changes


CBFpX

-210 -110 1

ε

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Django CDM

Rapgap MEPS

TBFpX

-210 -110 1

ε

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Django CDM

Rapgap MEPS

[GeV]CBFTP

-110 1 10

ε

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Django CDM

Rapgap MEPS

[GeV]TBFTP

-110 1 10

ε

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Django CDM

Rapgap MEPS

Figure 5.15: Efficiencies of K0S as functions of xp and pT in the current and the target

hemispheres of the Breit frame. The Django MC presented in red and the RapgapMC in blue.

2log Q2.2 2.4 2.6 2.8 3 3.2 3.4 3.6

rec

2 -

log

Qge

n2

log

Q

-0.04-0.03-0.02-0.01

00.01

0.020.030.04

genlog x

-2.5 -2 -1.5 -1 -0.5

rec

- lo

g x

gen

log

x

-0.04-0.03

-0.02-0.01

0

0.010.020.03

0.04

η-1.5 -1 -0.5 0 0.5 1 1.5

rec

η -

gen

η

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

[GeV]T

p1 10

T re

c -p

T ge

np

-1

-0.5

0

0.5

1

Figure 5.16: Resolutions as functions of Q2, x, η and pT variables in the laboratoryframe. The Django MC presented in red and the Rapgap MC in blue.


CBFpx

-210 -110 1

CBF

p ge

n -

xC

BFp

gen

x

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

TBFpx

-210 -110 1

TBF

p re

c -

xTB

Fp

gen

x

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

[GeV]CBFT

p

-110 1 10

[GeV

]C

BFT

rec

-pC

BFT

gen

p

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

[GeV]TBFT

p

-110 1 10 [G

eV]

TBF

T re

c -

pTB

FT

gen

p-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 5.17: Resolutions as functions of xCBFp , xTBF

p , pCBFT and pTBF

T variables inthe Breit frame. The Django MC presented in red and the Rapgap MC in blue.

is done varying each possible uncertain quantity under investigation by some reason-

able deviation in both sides, upward and downward, then all the analysis procedure

is repeated and the corresponding cross section is calculated again under the same

selection criteria in order to know the sensitivity of the applied cuts. Depending on

the kind of source the uncertainty is calculated using data and MC models or MCs

only.

The sources can be classified as reconstruction uncertainties if the source comes

from or depends on the reconstruction of the electron and hadronic final states parti-

cles (as the energy and the polar angle of the electron), the luminosity measurement,

the V0 finding efficiency and the topology reconstruction; and correction uncertain-

ties if they are applied to simulation models (model dependence), efficiencies (trigger

and track efficiency) or signal extraction.

The total uncertainty consists of the addition in quadrature of the systematic


and the statistic uncertainties:

∆σtot =

√

σ2stat +

∑

i

σ2i,sys.

where i runs over all sources of systematics uncertainties. When one is dealing with

differential cross section the uncertainties should be calculated for each bin.

The estimation of the systematic uncertainties expectations are detailed sepa-

rately in the following subsections.

5.3.1 Energy and polar angle of the electron

The energy and the polar angle of the scattered electron is used for the estimation

of the kinematic variables Q2, x and y but also for the boost to the Breit frame, so

a variation in the energy range can directly affect the K0S rate production.

The systematic effect due to the energy scale can be studied varying by ± 1%

the reconstructed energy on the LAr calorimeter. The resulting uncertainty for the

inclusive cross section is found to be +1.5 % and -2.9 %, a higher uncertainty when

the energy is down.

For the differential cross section the variation is calculated bin by bin, the un-

certainty plots as functions of variables in the laboratory and the Breit frames are

shown in Figures 5.18 and 5.19. It is observed that the uncertainties when the en-

ergy of the electron is varied up are between 0.2 and 2 % for most of the bins in the

laboratory frame but for the fist bin of Q2 the uncertainty is higher, up to around

8 %; when the energy of the electron is varied down the uncertainties are between 1

and 4 % except for the last two bins in x where the uncertainty goes to 8 %. In the

Breit frame the higher uncertainty appears in the current hemisphere with a higher

value of 7 % when the energy of the electron is varied down.

The resulting uncertainty, due to effects in the polar angle reconstruction of the

LAr Cal, is estimated to be +2.9% and -3.1% by changing the θe′ angle by ± 3 mrad.

Figures 5.20 and 5.21 present the uncertainties bin per bin in the laboratory and


the Breit frame variables, except for the bins in Q2 all the other plots show more

symmetry when the θe′ angle varies up and down.

]2 [GeV2Q310

[%]

σ) / e

(Eσ ∆

-4

-2

0

2

4

6

8 DownUp

X

-310 -210 -110

[%]

σ) / e

(Eσ ∆

-10

-8

-6

-4

-2

0

2

4

6

8DownUp

η-1.5 -1 -0.5 0 0.5 1 1.5

[%]

σ) / e

(Eσ ∆

-5

-4

-3

-2

-1

0

1

2

3

4 DownUp

[GeV]T

p1 10

[%]

σ) / e

(Eσ ∆-3

-2

-1

0

1

2

3

4DownUp

Figure 5.18: The systematic uncertainties due to the variation on the energy of thescaterred electron Ee′ as functions of the laboratory frame variables.

5.3.2 Luminosity

The uncertainty in the luminosity measurement (subsection 3.2.3) is not the same

for all year periods, for 2004 e+p it is 2.92 %, for 0405 e−p the value is 2.44 % and

2.69 % for the year 2006 e−p while it is 2.28 % for 0607 e+p period. At the end, the

contribution to the total systematic uncertainty for the HERA II data is taken to be

2.6 %.

5.3.3 Topology

The topology error comes from the difference in the seagull and sailor topologies

reconstruction efficiency. The uncertainty is estimated, first taking the ratio of the

K0S number extracted from the fit to the invariant mass distribution of the data and


CBFpx

-110 1

[%]

σ) / e

(Eσ ∆

-8

-6

-4

-2

0

2

4

6DownUp

TBFpx

-210 -110 1

[%]

σ) / e

(Eσ ∆

-6

-4

-2

0

2

4

6DownUp

[GeV]CBFT

p-110 1 10

[%]

σ) / e

(Eσ ∆

-6

-4

-2

0

2

4 DownUp

[GeV] TBFT

p-110 1 10

[%]

σ) / e

(Eσ ∆

-6

-4

-2

0

2

4

6DownUp

Figure 5.19: The systematic uncertainties due to the variation on the energy of thescattered electron Ee′ as functions of the Breit frame variables.

]2 [GeV2Q310

[%]

σ) / eθ(σ ∆

-12

-10

-8

-6

-4

-2

0

2

4

6

DownUp

x-310 -210 -110

[%]

σ) / eθ(σ ∆

-8

-6

-4

-2

0

2

4

6

8DownUp

η-1.5 -1 -0.5 0 0.5 1 1.5

[%]

σ) / eθ(σ ∆

-5

-4

-3

-2

-1

0

1

2

3

4

5DownUp

[GeV]T

p1 10

[%]

σ) / eθ(σ ∆

-6

-4

-2

0

2

4

6DownUp

Figure 5.20: The systematic uncertainties due to the variation on the polar angle ofthe scattered electron θe′ as functions of the laboratory frame variables.


CBFpx

-110 1

[%]

σ) / eθ(σ ∆

-6

-4

-2

0

2

4

6DownUp

TBFpx

-210 -110 1

[%]

σ) / eθ(σ ∆

-6

-4

-2

0

2

4

6DownUp

[GeV]CBFT

p-110 1 10

[%]

σ) / eθ(σ ∆

-6

-4

-2

0

2

4

6DownUp

[GeV]TBFT

p-110 1 10

[%]

σ) / eθ(σ ∆

-6

-4

-2

0

2

4

6DownUp

Figure 5.21: The systematic uncertainties due to the variation on the polar angle ofthe scattered electron θe′ as functions of the Breit frame variables.

the model Ri = N idata/N

imodel where i represents the topology types, seagull or sailor.

Then, the double ratio Rdouble = Rsailor/Rseagull leads to a uncertainty contribution.

A value of ± 3.0% is calculated for the visible inclusive cross section of the K0S . This

3 % is applied to all bins in the laboratory and the Breit frames.

5.3.4 Model dependence

The full analysis is corrected using Django MC which uses CDM as parton cas-

cade. To test the effect of the parton evolution scheme on the K0S production, the

analysis is also done using Rapgap with a different parton evolution (MEPS); A con-

tribution of ± 0.05 % to the total uncertainty is gotten by half of the ratio between

the difference in the efficiencies obtained from both models and the efficiency using

Django:

0.5 ∗ εCDM − εMEPS

εCDM.

The variations per bins in the laboratory and the Breit frame variables are seen


in Figures 5.22 and 5.23, the uncertainties oscillate between 0.1% to 1.2% in the

laboratory but it goes to higher values in the Breit frame, specially in the target

hemisphere where the values are between 0.1% and 3.4%.

]2 [GeV2Q310

[%]

σ(m

odel)

/ σ ∆

-1

-0.5

0

0.5

1

x-310 -210 -110

[%]

σ(m

odel)

/ σ ∆

-3

-2

-1

0

1

2

3

η-1.5 -1 -0.5 0 0.5 1 1.5

[%]

σ(m

odel)

/ σ ∆

-2

-1

0

1

2

3

[GeV]T

p1 10

[%]

σ(m

odel)

/ σ ∆

-3

-2

-1

0

1

2

3

Figure 5.22: The systematic uncertainties due to the variation on the model depen-dence as functions of the laboratory frame variables.

5.3.5 Track efficiency

The track efficiency uncertainty is considered due to the imperfection in the

reconstruction of the tracks that can mainly affect the K0S tag. In H1 detector, there

is no other component besides the central trackers to be used for checking the track

reconstruction efficiency, then a 2 % uncertainty is choosen for each track which is

determined by the tracks curling up at the CJC.

As two tracks compose the K0S, an uncertainty of ± 4 % (the sum of 2 % per track)

is considered for the total uncertainty calculation becoming the dominant systematic

error of the analysis. The same 4% value is applied to all bins in the laboratory and

the Breit frames.


CBFpx

-110 1

[%]

σ(m

odel)

/ σ ∆

-3

-2

-1

0

1

2

3

TBFpx

-210 -110 1

[%]

σ(m

odel)

/ σ ∆

-2

-1

0

1

2

3

[GeV]CBFT

p-110 1 10

[%]

σ(m

odel)

/ σ ∆

-3

-2

-1

0

1

2

3

[GeV]TBF T

p

-110 1 10

[%]

σ(m

odel)

/ σ ∆

-4

-3

-2

-1

0

1

2

3

Figure 5.23: The systematic uncertainties due to the variation on the model depen-dence as functions of the Breit frame variables.

5.3.6 Trigger efficiency

The uncertainty on the trigger efficiency is chosen to be ± 1 % as mentioned in

the first paragraph of the section 5.2.4, since the efficiency of the S67 trigger used in

this analysis is approximately 100 %. The same percentage is applied to all bins for

the uncertainty trigger contribution.

5.3.7 Signal extraction

The systematic effect of the signal extraction over the number of K0S candidates is

estimated using different procedures for the signal description. In the analysis, the fit

to a polynomial-exponential function for the background and a t-student distribution

for the signal were used, but the alternative way chosen to get the uncertainty here is

the side band subtraction method (SBS). The SBS gets the number of K0S candidates

by counting the number of events contained in the range [0.4 GeV, 0.6 GeV] around

the K0S mass peak from the original histogram of invariant mass distribution (without


any fit), then the number of background events is taken from the integral to the

background function previously used, in the same range [0.4 GeV, 0.6 GeV]. Then,

NSBSK0

S

= N signal

K0S

(counting the histogram)−N bgrd

K0S

(integral to background function) is

the number of K0S candidates from the SBS method.

The resulting uncertainty is finally gotten from the ratio:

N fit

K0S

− NSBSK0

S

N fit

K0S

,

where N fit

K0S

is the number of K0S from the signal extraction as discussed in section 4.6.

For the total HERA II systematic determination the contribution is ± 2.0 %.

]2 [GeV2Q310

[%]

σ(si

gnal)

/ σ ∆

-1

0

1

2

3

4

5

6

x-310 -210 -110

[%]

σ(si

gnal)

/ σ ∆

-3

-2

-1

0

1

2

3

η-1.5 -1 -0.5 0 0.5 1 1.5

[%]

σ(si

gnal)

/ σ ∆

-3

-2

-1

0

1

2

3

[GeV]T

p1 10

[%]

σ(si

gnal)

/ σ ∆

-3

-2

-1

0

1

2

3

Figure 5.24: The systematic uncertainties due to the variation on the signal extrac-tion as functions of the laboratory frame variables.

The plots of the uncertainty variation due to signal extraction bin by bin are in

Figures 5.24 and 5.25. The oscillation of the values shows the difficulties to obtain

a fit of better quality to the mass invariant distribution, per example the last bin in

Q2 (Figure F.1) and xTBFp (Figure F.6) and the first bin of pTBF

T (Figure F.8).


CBFpx

-110 1

[%]

σ(si

gnal)

/ σ ∆

-3

-2

-1

0

1

2

3

TBFpx

-210 -110 1

[%]

σ(si

gnal)

/ σ ∆

-18-16-14-12-10-8-6-4-202

[GeV]CBF T

p-110 1 10

[%]

σ(si

gnal)

/ σ ∆

-3

-2

-1

0

1

2

[GeV]TBFT

p-110 1 10

[%]

σ(si

gnal)

/ σ ∆

-12

-10

-8

-6

-4

-2

0

2

Figure 5.25: The systematic uncertainties due to the variation on the signal extrac-tion as functions of the Breit frame variables.

5.3.8 Branching ratio

This uncertainty is taken into account because the branching ratio of the K0S de-

caying to π+π− is not exactly known, the PDG reports a BR = (0.6920 ± 0.0005)% [11],

then ± 0.1% is considered for the contribution to the total uncertainty determina-

tion. As this contribution is very small, it could be neglected. The same uncertainty

values is applied to all bins in the laboratory and the Breit frames.

All sources contributing to the total systematic uncertainty for the measured

inclusive K0S cross section from the HERA II data are listed in Table 5.3; the variation

used for the estimation and the ∆σ obtained are also presented. It is possible to

distinguish that the dominat contributions come from the topology reconstruction,

the Θe′ variation and the track efficiency reconstruction. At the end, a systematic

uncertainty of +6.9 % and -7.4 % is estimated.


Table 5.3: Summary of systematic uncertainties.

Source Variation ∆σ(K0s )

E ′

e′ 1 % +1.5%/−2.9%

Θe′ ± 3 mrad +2.9%/−3.1%

signal extraction Nfit−NSBS

Nfit ± 2.0%

model dependence 0.5* εCDM−εMEPS

εCDM ± 0.05 %topology rec ± 3.0 %

luminosity ± 2.6 %

track rec 2 % per track ± 4.0 %

branching ratio ± 0.1 %

trigger efficiency ± 1.0 %

total uncertainty +6.9%/−7.4%

The statistical uncertainty is obtained by:

σstat. =

√

(σNK0

s

NK0s

)2

data

+

(σNK0

s

NK0s

)2

rec−MC

(5.6)

where NK0s

is the number of K0S extracted from the fit and σN

K0s

is the statistical

uncertainty from the fit procedure.

As NK0s

= 38154 and σNK0

s= 1194 for data, and NK0

s= 39984 and σN

K0s

= 233

for reconstructed-MC, a total statistical uncertainty of ∼ 3 % is calculated.

Chapter 6

Results and conclusions

The measurements of the inclusive K0S meson cross section as total, differential

and double–differential are presented in this chapter. The cross section ratio of the

K0S over the charged particles, and the density measurements are also calculated and

explained here.

The comparison to Django (CDM) and Rapgap (MEPS) model predictions are

shown in all plots in order to establish if the data favour any model or strangeness

suppresion factor λs value. The Django model is used for the QCD studies varying

the PDF and λs parameters, while Rapgap is chosen for the study of the quark

flavour contribution to the K0S cross section.

6.1 Total K0s cross section

The inclusive K0S production cross section σvis measured in the visible range

defined by the phase space in equation 5.1 is found to be:

σvis = 531 ± 17 (stat)+37−39 (sys) pb, (6.1)

where the efficiency ε ∼ 30.55% with the included QED correction δQED ∼ 5.5% as

determined in the subsection 5.2.4, the BR = 0.692 from the Table 2.2 for the K0S

→ π+π− decay channel, the luminosity value of 339.6 pb−1 as listed in the Table 4.1

107

108 CHAPTER 6. RESULTS AND CONCLUSIONS

and the NK0S

= 38154 as extracted from the fit in Figure 4.4 are used for the cross

section determination with the equation 5.2. The statistical (3 %) and systematic

uncertainties (+6.9 % and -7.4 %) obtained in the subsection 5.3, are calculated from

the application of the corresponding percentage to the cross section.

The predictions of Django and Rapgap Monte Carlo programs with different

strangeness values λs but same CTEQ6L PDF were estimated giving the cross sec-

tions values presented in the Table 6.1. The statistical errors are very small since

the luminosity of the non-radiative MCs used for the predictions (sections 1.4.1 and

1.4.2) is around 74 times larger than the luminosity of data (339.6 pb−1).

Table 6.1: The Monte Carlo cross section predictions for different strangeness sup-presion factors (λs).

λs = 0.22 λs = 0.286 λs = 0.3

Django (CDM) σ = 443 pb σ = 516 pb σ = 518 pb

Rapgap (MEPS) σ = 444 pb σ = 536 pb σ = 519 pb

The Monte Carlo predictions are in good agreement with the measurement within

the uncertainties, specially with λs = 0.286 and λs = 0.3, while the predictions with

λs = 0.22 for both models underestimate the measurement.

The inclusive cross section was calculated year by year to look for stability of the

measurement. In Figure 6.1, the visible cross section σvis measured for all HERA II

data (equation 6.1) is represented with a black dashed line, the statistical uncertainty

forms the shadow rectangle around the σvis value. The measured cross section per

period are depicted as blue points with their respective statistical uncertainty, while

the cross sections obtained with the Django Monte Carlo are plotted with red points.

It is found that the measurements per period are consistent with the cross section

estimated with the full data sample.

The measured ratio of the inclusive cross section of the K0S meson over the charged

6.2. DIFFERENTIAL K0S CROSS SECTION 109

Year2004 2005 2006 2007

Cro

ss S

ectio

n [p

b]

400

450

500

550

600

650 Data HERA IIDataModel CDM

Figure 6.1: Inclusive cross section for the four year periods of HERA II data. Themeasurement (in blue) presented with statistical uncertainty is compared to the pre-diction of the Django model (in red). The measured cross section for the full HERA IIdata is shown in the black line with the shadow being its statistical uncertainty.

particle production:

σvis(ep → eK0SX)

σvis(ep → eh±X)= 0.05867 ± 0.0019 (stat) ± 0.0024 (sys), (6.2)

is in agreement (within the uncertainties) with the prediction of the CDM model:

0.05922. It is also consistent with the results obtained from the analysis at low Q2,

presented in subsection 2.5.

The density ratio gives a measurement of:

σvis(ep → eK0SX)

σvis(ep → eX)= 0.3842 ± 0.0115 (stat) ± 0.0159 (sys), (6.3)

and the prediction of Django gives 0.3988, showing good consistency.

6.2 Differential K0s cross section

The differential cross section in the laboratory frame as functions of the four-

momentum of the virtual photon Q2, the Bjorken scaling variable x, the pseudo-

rapidity η of the K0S, and the transverse momentum pT of the K0

S are shown in


Figure 6.2, where the cross section graphs are placed in the upper part of each plot,

while the ratio between the models and data for the two strangeness factor (λs = 0.22

and λs = 0.286) for Django and Rapgap are presented in the bottom of each plot in

order to have a better visualization of the comparisons.

The measurement decreases quickly when Q2 and pT take higher values. While

the behaviour as functions of x and η is a small increasing that then falls down.

The data are better described by the models with λs = 0.286 in normalization and

shape, independenly of the MC model, since both Django and Rapgap give similar

descriptions. The models with λs = 0.22 subestimate the measurements in most of

the bins. The results are bin-averaged and no bin-center corrections are applied.

The corresponding differential K0S cross section in the Breit frame as function of

the scaled momentum fraction xBFp and the K0

S transverse momentum pBFT in the

current (CBF) and the target (TBF) hemispheres are shown in Figure 6.3. The

production decreases at high values of the variables. The comparison to Django and

Rapgap Monte Carlo programs shows good description of data by the models with

λs = 0.286 in the current region were the preferred production mechanism is the

hard interaction process, while in the target region the models allow to observe some

sensitivity to the λs factor, as expected due to the domination of the hadronization

process in this hemisphere of the BF. The differential cross sections together with

statistical, systematic uncertainties and the CDM model prediction values can be

found in the Tables 6.2 and 6.3.

6.3 Ratios of the differential cross sections

Due to the cancellation of some uncertainty sources the total uncertainty is re-

duced for the cross section ratios, for instance the K0S cross section over the charged

particle production and the K0S over the DIS cross section ratios. Therefore the ra-

tios are used for looking at global description of all observed cross sections or test

different aspects of the meson production within the fragmentation models. They

6.3. RATIOS OF THE DIFFERENTIAL CROSS SECTIONS 111

]2 [GeV2Q

310

MC

/Da

ta

0.70.80.9

11.11.2

3

]2

[p

b/G

eV

2/d

Qσ

d

-210

-110

1


=0.22)sλMEPS (=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary

Xs0 e K→ep

x-310 -210 -110

MC

/Da

ta

0.70.80.9

11.11.2

-3

/dx [

pb

]σ

d

210

310

410

510


=0.22)sλMEPS (=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary

Xs0 e K→ep

η-1.5 -1 -0.5 0 0.5 1 1.5

MC

/Da

ta

0.70.80.9

11.11.2 -1.5 -1 -0.5 0 0.5 1 1.5

[p

b]

η/d

σd

50100150200250300350400450


=0.22)sλMEPS (=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary

Xs0 e K→ep

[GeV]T

p1 10

MC

/Da

ta

0.70.80.9

11.11.2

[p

b/G

eV

]T

/dp

σd

1

10

210


=0.22)sλMEPS (=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary Xs

0 e K→ep

Figure 6.2: Cross sections of the K0S meson in the laboratory frame as functions

of the four-momentum of the virtual photon Q2, the Bjorken scaling variable x,the pseudorapidity η of the K0

S, and the transverse momentum pT of the K0S. The

comparisons are clearer in the MC model over data ratio plotted in the bottom ofeach plot. The outer (inner) error bar indicates the total (statistical) uncertainty.


ep → eK0

sX

Q2 dσ/dQ2 stat. syst. (+) syst. (−) MC Pred

[GeV2] [pb/GeV2]

145 – 167 4.12 0.30 0.45 0.54 3.88

167 – 200 2.67 0.16 0.17 0.18 2.73

200 – 280 1.59 0.10 0.11 0.12 1.54

280 – 500 0.58 0.04 0.04 0.04 0.55

500 – 1000 0.14 0.02 0.008 0.008 0.12

1000 – 5000 0.010 0.002 0.0007 0.0007 0.008

x dσ/dx stat. syst. (+) syst. (−) MC Pred

[pb]

0.0 – 0.004 18595 1180 1860 1674 18087.4

0.004 – 0.008 56023 2631 3361 3361 55195.1

0.008 – 0.017 17479 1205 1398 1923 16217.8

0.017 – 0.20 405 39 28 41 414.853

η dσ/dη stat. syst. (+) syst. (−) MC Pred

[pb]

-1.5 – -0.5 96.6 6.41 6.18 6.7 91.5

-0.5 – 0.0 244.6 21.8 15.7 16.4 215.3

0.0 – 0.45 263.2 23.7 17.9 18.9 245.3

0.45 – 0.95 216.3 14.3 16.4 17.3 215.9

0.95 – 1.5 165.3 11.5 12.9 13.9 178.8

pT dσ/dpT stat. syst. (+) syst. (−) MC Pred

[GeV] [pb/GeV]

0.3 – 0.8 285.0 17.8 19.7 21.1 297.3

0.8 – 1.1 228.8 14.2 15.6 16.7 244.7

1.1 – 1.55 172.9 9.6 11.8 12.6 173.8

1.55 – 2.23 115.6 7.8 7.9 8.4 108.7

2.23 – 3.5 63.0 5.5 4.5 4.8 55.3

3.5 – 14.0 7.18 0.8 0.5 0.55 6.6

Table 6.2: The differential K0s cross section values as functions of Q2, x, η and pT

in the visible kinematic region defined by 145 < Q2 < 20000 GeV2, 0.2 < y < 0.6,-1.5 η(K0

S) 1.5 and pT > 0.3 GeV. The bin ranges, the bin averaged cross sectionvalues, the statistical and the positive and negative systematic uncertainties, as wellas the predictions from Django are listed.


CBFpx

-110 1

MC

/Da

ta

0.60.8

11.21.4

[p

b]

CB

Fp

/dx

σd

10

210

310

410


=0.22)sλMEPS (=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary

X (Breit Frame)s0 e K→ep

TBFpx

-110 1

MC

/Da

ta

0.60.8

11.21.4

[p

b]

TB

Fp

/dx

σd

10

210

310

410


=0.22)sλMEPS (=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary


[GeV]CBFT

p

-110 1 10

MC

/Da

ta

0.60.8

11.21.4 -1

[p

b/G

eV

]C

BF

T/d

pσ

d

1

10

210

310


=0.22)sλMEPS (=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary


[GeV]TBFT

p

-110 1 10

MC

/Da

ta

0.60.8

11.21.4 -1

[p

b/G

eV

]T

BF

T/d

pσ

d

1

10

210

310


=0.22)sλMEPS (=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary


Figure 6.3: Cross section of the K0S meson in the Breit frame as function of the scaled

momentum fraction and the transverse momentum in the current region (xCBFp and

pCBFT in the left hand side of the figure) and the target region (xTBF

p and pTBFT in

the right hand side). The outer (inner) error bar indicates the total (statistical)uncertainty. More details in caption of Figure 6.2


ep → eK0

sX

xBreitp current dσ/dxBreit

p stat. syst. (+) syst. (−) MC Pred

[pb]

0.0 – 0.07 859.1 78.8 56.6 64.3 848.4

0.07 – 0.13 1339.5 102.6 90.9 107.0 1202.1

0.13 – 0.2 879.2 84.5 61.5 71.9 805.4

0.2 – 0.33 458.1 38.3 32.0 42.2 385.1

0.33 – 1.0 56.7 5.9 4.5 5.7 45.7

xBreitp target dσ/dxBreit

p stat. syst. (+) syst. (−) MC Pred

[pb]

0.0 – 0.07 557.7 88.4 50.1 46.8 522.5

0.07 – 0.13 859.1 59.0 67.8 63.5 929.7

0.13 – 0.2 625.7 52.6 46.2 44.9 721.6

0.2 – 0.33 356.3 29.7 25.6 23.5 388.2

0.33 – 1.0 72.9 6.7 5.6 5.3 71.3

1.0 – 2.0 3.4 0 0.6 0.6 4.9

pBreitT current dσ/dpBreit

T stat. syst. (+) syst. (−) MC Pred

[GeV] [pb/GeV]

0.0 – 0.35 200.2 19.2 13.6 17.4 190.9

0.35 – 0.6 288.7 26.4 21.0 24.8 258.2

0.6 – 1.0 180.8 11.3 12.3 14.9 159.0

1.0 – 1.8 65.2 6.5 4.6 5.2 58.9

1.8 – 14.0 2.3 0.3 0.15 0.2 2.18

pBreitT target dσ/dpBreit

T stat. syst. (+) syst. (−) MC Pred

[GeV] [pb/GeV]

0.0 – 0.35 86.45 23.9 11.2 12.1 74.1

0.35 – 0.6 191.4 18.9 15.3 14.3 204.5

0.6 – 1.0 150.7 9.6 11.3 10.5 167.4

1.0 – 1.8 67.6 4.7 4.9 4.7 71.5

1.8 – 14.0 3.8 0.5 0.3 0.3 3.7

Table 6.3: The differential K0S cross-section values as functions of pBreit

T and xBreitp

in the current and target hemispheres of the Breit frame. More details in caption ofTable 6.2.


also provide a rather direct constrain of λs, or/and λqq and λsq.

6.3.1 Differential K0S/h± cross section

The K0S/h± cross section, defined as the ratio of the K0

S production over the

charged particle cross section measured in the same phase space as the K0S, were

determined in the laboratory frame as shown in Figure 6.4. The measured production

shows an almost flat ratio as function of Q2; as function of η there is a small falling,

and as function of pT rises at higher values due to the K0S, which takes most of the

momentum than the usually lower massive charged particles.

The shape and normalization of the ratios are reasonably well described by the

CDM and MEPS models with λs = 0.286 for the four plots. The values of the

ratio cross sections, the statistical and systematic uncertainties and the CDM model

predictions for each bin can be found in Table 6.4.

6.3.2 Differential K0s/DIS cross section

The density plots, defined as the ratio between the cross section of the K0S and

the DIS event production in the same kinematic region as the K0S, are measured

differentially as functions of Q2 and x as shown in Figure 6.5. The K0S multiplicity

average lies at ∼ 0.4 independenly of the variables, indicating that the K0S production

fraction with respect to the DIS events is almost equal at any region. The Django

and Rapgap models with λs = 0.286 describe quite well the measurements in Q2 but

they predict a small falling as function of x which is not observed from data. The

cross section values of the ratio with their corresponding statistical and systematic

uncertainties as well as the CDM model predictions bin by bin can be found in

Table 6.5.


]2 [GeV2Q310

X)

± e

h→

(ep

σ

X)/

ds0

eK

→(e

p

σd

0

0.02

0.04

0.06

0.08

0.1

0.12H1 Data

=0.22)sλCDM (

=0.22)sλMEPS (=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary

X ± e h→ X / ep s0 e K→ep

x-310 -210 -110

X)

± e

h→

(ep

σ

X)/

ds0

eK

→(e

p

σd

0

0.02

0.04

0.06

0.08

0.1

0.12H1 Data

=0.22)sλCDM (

=0.22)sλMEPS (=0.286)sλCDM (=0.286)sλMEPS (

H1 preliminary


η-1.5 -1 -0.5 0 0.5 1 1.5

X)

± e

h→

(ep

σ

X)/

ds0

eK

→(e

p

σd

0

0.02

0.04

0.06

0.08

0.1

0.12H1 Data

=0.22)sλCDM (=0.22)sλMEPS (

=0.286)sλCDM (=0.286)sλMEPS (

H1 preliminary


[GeV]T

p1 10

X)

± e

h→

(ep

σ

X)/

ds0

eK

→(e

p

σd

0

0.02

0.04

0.06

0.08

0.1

0.12H1 Data

=0.22)sλCDM (

=0.22)sλMEPS (

=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary


Figure 6.4: Ratio between the cross sections of the K0S and the charge particles

in the laboratory frame as functions of Q2, x, η and pT . The outer (inner) errorbar indicates the total (statistical) uncertainty. The CDM and MEPS models withλs = 0.22 and λs = 0.286 are presented for comparison.


R(K0

s/h±)

Q2 R(K0

s /h±) stat. syst. MC Pred

[GeV2]

145 – 167 0.0620 0.00464 0.00240 0.0614

167 – 200 0.0574 0.00353 0.00214 0.0610

200 – 280 0.0601 0.00382 0.00221 0.0604

280 – 500 0.0588 0.00382 0.00214 0.0590

500 – 1000 0.0588 0.00657 0.00219 0.0566

1000 – 5000 0.0585 0.01273 0.00345 0.0522

x R(K0


0.0 – 0.004 0.0596 0.00378 0.00229 0.0615

0.004 – 0.008 0.0592 0.00278 0.00216 0.0608

0.008 – 0.017 0.0609 0.00420 0.00236 0.0588

0.017 – 0.20 0.0492 0.00477 0.00185 0.0540

η R(K0


-1.5 – -0.5 0.0628 0.00417 0.00237 0.0642

-0.5 – 0.0 0.0619 0.00552 0.00254 0.0590

0.0 – 0.45 0.0585 0.00527 0.00228 0.0574

0.45 – 0.95 0.0560 0.00371 0.00210 0.0574

0.95 – 1.5 0.0537 0.00375 0.00232 0.0593

pT R(K0


[GeV]

0.3 – 0.8 0.0357 0.00223 0.00154 0.0392

0.8 – 1.1 0.0553 0.00343 0.00227 0.0607

1.1 – 1.55 0.0673 0.00375 0.00249 0.0696

1.55 – 2.23 0.0794 0.00536 0.00294 0.0777

2.23 – 3.5 0.0906 0.00796 0.00372 0.0849

3.5 – 14.0 0.0880 0.00922 0.00352 0.0884

Table 6.4: The values of the ratio of the differential production cross sections formesons and charged hadrons as functions of Q2, x, pT and η. More details in captionof Table 6.2.


]2 [GeV2Q310

e X

)→

(ep

σ X

)/s0

e K

→(e

p σ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


=0.22)sλMEPS (

=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary

e X → X / ep s0 e K→ep

x-310 -210 -110

e X

)→

(ep

σ X

)/s0

e K

→(e

p σ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


=0.22)sλMEPS (

=0.286)sλCDM (

=0.286)sλMEPS (

H1 preliminary

e X → X / ep s0 e K→ep

Figure 6.5: Density plots in the laboratory frame as functions of Q2 and x. Theouter (inner) error bar indicates the total (statistical) uncertainty. The CDM andMEPS models with λs = 0.22 and λs = 0.286 are presented for comparison.

6.4. DOUBLE DIFFERENTIAL CROSS SECTION 119

R(K0

s/X)

Q2 R(K0

s /X) stat. syst. MC Pred

[GeV2]

145 – 167 0.3801 0.02852 0.01459 0.4001

167 – 200 0.3581 0.02210 0.01332 0.4022

200 – 280 0.3862 0.02460 0.01421 0.4048

280 – 500 0.3943 0.02568 0.01435 0.4045

500 – 1000 0.4102 0.04588 0.01530 0.3947

1000 – 5000 0.4161 0.09060 0.02455 0.3573

x R(K0

s /X) stat. syst. MC Pred

0.0 – 0.004 0.3943 0.02513 0.01510 0.4340

0.004 – 0.008 0.3816 0.01797 0.01393 0.4108

0.008 – 0.017 0.3936 0.02718 0.01527 0.3894

0.017 – 0.20 0.3352 0.03250 0.01257 0.3577

Table 6.5: Values of the differential production cross section ratio of the K0S mesons

and the deep inelastic scattering events as function of Q2 and x in the laboratoryframe. More details in caption of Table 6.2.

6.4 Double differential cross section

The double differential cross section of K0S as functions of Q2 and xCBF

p normalized

to the σvis of the corresponding Q2 range is presented in Figure 6.6 for three different

ranges of Q2 and five bins of xCBFp .

In the Figure is possible to see that the K0S production grows up as the Q2 range

is larger and the increase is more significant at low xCBFp values, which is the same

behavior observed for the fragmentation functions in e+e− annihilation and DIS as

shown in reference [11].

The Django (CDM) model with λs = 0.286 chosen for the comparison describes

quite well the measurements.

6.5 Comparison to QCD models

Thanks to the many parameters found in the models, it is possible to do some

additional studies, mainly changing the most relevant parameter values for the K0S


CBFpX

-210 -110 1

X)

s0 e

K→

(ep

σ d

DIS

σ1/

-210

-110

1

2H1 Data 145 < Q2 < 200 GeV2H1 Data 200 < Q2 < 500 GeV

2H1 Data 500 < Q2 < 5000 GeV2CDM 145 < Q2 < 200 GeV2CDM 200 < Q2 < 500 GeV

2CDM 500 < Q2 < 5000 GeV

e X→ X / ep s0 e K→ep

Figure 6.6: Double differential cross section in bins of xCBFp in three different ranges

of Q2. The comparison to Django model shows good agreement.

production and comparing the results of the predictions to data. Previously, two

different values of strangeness suppresion factor for Django and Rapgap were pre-

sented, now the parton density function PDF is changed in the Django model with

λs = 0.286.

The study of disentangling the flavour contribution of the K0S production is carried

out using the Rapgap model with λs = 0.286.

6.5.1 Parton distribution functions

In order to test for possible dependencies of the K0S strange meson production on

the proton parton density functions (PDFs), the measured K0S cross sections are com-

pared to the CDM model with λs = 0.286 using three different PDF parametrizations,

CTEQ6L, H12000L0 and GRVL0, as shown in Figure 6.7. The model descriptions

are similar in shape for the three PDFs but in normalization only the CTEQ6L and

H12000LO PDFs agree with data, while GRVLO98 underestimates considerably the

measurements due to the absence of c and b flavour. Then, one could uses GRVLO98

6.6. CONCLUSIONS 121

PDF as an estimation of the contribution of c and b quarks to the total K0S produc-

tion to understand or quantify the mechanisms of production from these quarks.

Similar results are obtained in the Breit frame.

6.5.2 Flavour contribution

The flavour contributions to the K0S cross section are investigated using the Rap-

gap (MEPS) prediction with λs = 0.286. The choice was made because a separation

between the QPM, QCDc and BGF production mechanism are possible with this

model but not with Django (CDM).

Figures 6.8 and 6.9 show the contribution of the different flavours in the labo-

ratory and the Breit frames, respectively. The light ud quarks contribution from

fragmentation mechanism dominates for all variables, then the main contribution

process is due to hadronization. The heavy quark contribution of charm c is highest

that the one of bottom flavour b which goes to zero or close to zero in some bins;

both (c and b) make the second dominat contribution coming mainly from the heavy

decay process. The s contribution remains to be the lowest in all variables but it

becomes more relevant at high values of Q2, x and pT (see the logarithm scale) while

in η is almost constant, here the production processes are the boson gluon fusion and

the QPM hard interaction.

As functions of the Breit frame variables, the s contribution becomes more impor-

tant at high xp and pT values, specially in the current region where the contribution

as function of xCBFp even equals the heavy quark contribution.

The contributions can be approximately quantified as 52% of the K0S coming from

ud, 36% from cb quarks and only a 12% from s quarks.

6.6 Conclusions

The K0S meson production in the phase space defined by 145 < Q2 < 20000 GeV,

0.2 < y < 0.6, -1.5 < η(K0S) < 1.5 and 0.3 GeV < pT (K0

S) presented in this thesis cor-


]2 [GeV2Q

310

MC

/Da

ta

0.6

0.8

13

]2

[p

b/G

eV

2/d

Qσ

d

-210

-110

1

H1 Data=0.286)λCTEQ6L (=0.286)λGRVL098 (=0.286)λH12000L0 (

Xs0 e K→ep

x-310 -210 -110

MC

/Da

ta

0.6

0.8

1-3

/dx [

pb

]σ

d

210

310

410

510


Xs0 e K→ep

η-1.5 -1 -0.5 0 0.5 1 1.5

MC

/Da

ta

0.6

0.8

1-1.5 -1 -0.5 0 0.5 1 1.5

[p

b]

η/d

σd

50

100

150

200

250

300

350

400

450H1 Data

=0.286)λCTEQ6L (=0.286)λGRVL098 (=0.286)λH12000L0 (

Xs0 e K→ep

[GeV]T

p1 10

MC

/Da

ta

0.6

0.8

1

[p

b/G

eV

]T

/dp

σd

1

10

210

310


Xs0 e K→ep

Figure 6.7: Comparison of cross section to three different PDFs: CTEQ6L,GRVLO98 and H12000LO in the laboratory frame as functions of Q2, x, η andpT . No dependence is found between CTEQ6L and H12000LO, the underestimationof GRVLO98 is due to the absence of the charm and beauty quark contribution.


]2 [GeV2Q310

]2

[p

b/G

eV

2/d

Qσ

d

-310

-210

-110

1

10

H1 Dataudscbudscb

H1 preliminary

Xs0 e K→ep

x-310 -210 -110

/dx [p

b]

σd

210

310

410

510

H1 Dataudscbudscb

H1 preliminary

Xs0 e K→ep

η-1.5 -1 -0.5 0 0.5 1 1.5

[p

b]

η/d

σd

50

100

150

200

250

300

350

400

450H1 Dataudscbudscb

H1 preliminary

Xs0 e K→ep

[GeV]T

p1 10

[p

b/G

eV

]T

/dp

σd

1

10

210

310

H1 Dataudscbudscb

H1 preliminary

Xs0 e K→ep

Figure 6.8: Flavour contribution of the light ud quarks, the strange s quark andthe heavy cb quarks to the K0

S cross section studied with the Rapgap model in thelaboratory frame as functions of Q2, x, η and pT . The outer (inner) error bar indicatesthe total (statistical) uncertainty.


CBFpx

-310 -210 -110

[p

b]

CB

Fp

/dx

σd

1

10

210

310

H1 Dataudscbudscb

H1 preliminary


TBFpx

-210 -110 1

[p

b]

TB

Fp

/dx

σd

1

10

210

310

H1 Dataudscbudscb

H1 preliminary


[GeV]CBFT

p-110 1 10

[p

b/G

eV

]C

BF

T/d

pσ

d

1

10

210

310

H1 Dataudscbudscb

H1 preliminary


[GeV]TBFT

p-110 1 10

[p

b/G

eV

]T

BF

T/d

pσ

d

1

10

210

310

H1 Dataudscbudscb

H1 preliminary


Figure 6.9: Flavour contribution of the light ud quarks, the strange s quark and theheavy cb quarks to the K0

S cross section studied with Rapgap model in the Breitframe as functions of xCBF

p , xTBFp , pCBF

T and pTBFT . The outer (inner) error bar

indicates the total (statistical) uncertainty.


responds to the first measurement of the H1 collaboration in the high Q2 range [79].

The production is studied total and differentially in the laboratory and the Breit

frames.

The Django and Rapgap DIS events simulation programs are used with matrix

elements plus colour dipole model and parton showers, respectively. The CTEQ6L

parton distribution function and strangeness suppresion factor λs with ALEPH tun-

ning are taken for corrections. The comparison of Monte Carlo to data shows good

agreement in general features for all variables.

]2 [GeV2Q1 10 210 310 410

]2 [

nb

/Ge

V2

/dQ

σd

-610

-510

-410

-310

-210

-110

1

10 H1 DataDjango CDMRapgap MEPS

Figure 6.10: Cross section production of K0S at low Q2 [66] and high Q2 ranges

compared to the Django and Rapgap simulation programs with λs = 0.3 for low Q2

results and λs = 0.286 for high Q2.

The shape of the differential K0S production in the laboratory and the Breit frames

are similar to those obtained at low Q2 analysis, as discussed in the subsection 2.5.3,

although the data in that case were better described with λs = 0.3.

Figure 6.10 presents the results obtained at low Q2 analysis [66] and the ones


measured at high Q2 range as done in this thesis (in the same phase space defined

at the low Q2 analysis) and the two Monte Carlo predictions taken into account. It

is possible to see agreement between the measurements and theory. The decreasing

behavior of the K0S production continues from low to high Q2 values due to the 1/Q4

factor in the cross section formula.

The ratio of the K0S over the charged particle productions and the so called den-

sity, the ratio of the K0S over the DIS event cross sections, are measured differentially

in the laboratory frame. They show almost flat behavior indicating the same rate of

production in all regions of the H1 phase space considered here. As function of pt,

there is an increase, which is expected due to the higher mass of the K0S compared

to the charged particles which are mainly pions.

The Django model with λs = 0.286 and CTEQ6L, H12000LO and GRVLO98

parton density functions are used for the study of the PDF dependence, but no

evidence of dependence is found between CTEQ6L and H12000LO PDFs. In other

hand, the GRVLO98 PDF underestimates the results due to the absence of the charm

and beauty quark contributions.

The cross section separated by flavour contributions is studied with the Rapgap

model with λs = 0.286 and CTEQ6L PDF. It is found that the K0S production is

dominated by the hadronization process (ud quarks contribution) but the s quark

contribution becomes more important at high momentum values, which is consistent

with the conclusion of the K∗ analysis, as mentioned in the section 2.5.2.

Further studies will be focus in the production ratio of strange baryons to strange

mesons (Λ/K0S) for a better understanding of the di-quarks pair production in the

Lund string model. The ratio of the production of vector to pseudoscalar mesons

(K∗/K0s ) could provides some information about the relative probabilities for the

corresponding spin states which to be produced on the hadronization process. Studies

of asymmetric quark sea in the proton can be carried out analysing the difference in

the production of charged kaons (as K∗+ and K∗−). As well, as the studies of K0SK0

S

states and resonances which have K0S particles in their decays channels can be done


to improve the current knowledge of strangeness physics.


Appendix A

Reconstruction methods

The methods of reconstruction at HERA physics are governed by the two body

elastic collision. The final states can be completely reconstructed using two variables

when the energies of the initial particles are known, the energy of the incident electron

(Ee) and proton (Ep) in the case of H1.

The variables of a DIS event can be determined by two of the following inde-

pendent variables: the energy of the scattered electron (E ′), its polar angle (θe′) or

some quantities reconstructed out of the hadronic final state particles, as the four-

momentum conservation Σh =∑

h(Eh−pz,h) of each particle (h, the total transverse

momentum (pT,h) or the angle of the scattered quark (γ) within QPM:

Σh =∑

h

(Eh − pz,h) , pT,h =

√

(∑

h

px,h)2 + (∑

h

py,h)2, tanγ

2=

Σh

pT,h

.

There are three basic methods of reconstruction, the electron e, the hadron h and

the double angle (DA) methods. However mixtures of them have been created in

order to optimize the calculation of the kinematic variables [80]. A brief description

of the most known methods can be found in the next sections.

A.1 The electron method

As its name indicates, this method uses only the information of the electron, Ee,

E ′

e and θe measured by the electromagnetic section of the calorimeters, to calculate

129

130 APPENDIX A. RECONSTRUCTION METHODS

the kinematic variables, the four-momentum transfer Q2, the inelasticity y and the

Bjorken-x:

Q2 = 4EeE′ecos2 θe

2, ye = 1 − Ee

2E ′e

(1 − cos2 θe

2), xe =

Q2e

sye

.

At high y, where the electron is very well detected by the CTD and the SpaCal,

this method provides a high precision, but at low y it is not due to the 1/y dependence

of the resolution (δy/y). In the case of initial state radiation (ISR) the energy of

the electron is reduced from Ee, thus Q2 and y are overestimated, while x suffers a

degradation.

A.2 The hadron method

This method, also called Jacquet-Blondel method, makes use of Σh and pT,h

for the reconstruction. For this reason, it is mainly used for charged current DIS

events, because the scattered neutrino is undetected and the kinematic variables

determination lies on the hadronic final states measured by the calorimeters:

Q2h =

p2T,h

1 − yh

, yh =Σh

2Ee

, xh =Q2

h

syh

.

The angle γ of the hadronic final states is determined as:

cosγ =Q2

h(1 − yh) − 4E2ey

2h

Q2h(1 − yh) + 4E2

ey2h

.

A.3 The double angle method

The DA method reconstruct the kinematic variables using only the θe and γ

angles. If the energy measured is considered as continuous over the full solid angle,

the event kinematics are independent of any calorimetric energy scale uncertainties:

Q2DA =

4E2esenγ(1 + cosθe)

senγ + senθe − sen(θe + γ), (A.1)

yDA =senθe(1 − cosγ)

senγ + senθe − sen(θe + γ),

A.4. THE SIGMA METHOD 131

xDA =Q2

DA

syDA

.

A.4 The sigma method

The sigma method, Σ, compensates for the cases where missing energy exits

due to ISR. The photon is usually undetected because travels in the same electron

beam direction and escapes out of the beam pipe. What it does is to balance the

missed energy by a factor calculated by conservation of longitudinal momentum of

the hadronic and the detected electron energies. Then, y and Q2Σ are independent of

ISR-QED and the resolution is optimal. The kinematics is formulated like:

Q2Σ =

P 2T,e

1 − yΣ

, yΣ =Σh

Σ, xΣ =

Q2Σ

syΣ

Another good point is that the experimental errors on Σh measurements cancel

between numerator and denominator at high y, where Σh becomes dominant.

A.5 The electron-sigma method

The eΣ method [81] improves the imprecise reconstruction of Q2Σ and xe using

Q2e and xΣ, respectively. In that way, the precision at high y is also improved. Then:

Q2eΣ = Q2

e, yeΣ =Q2

Σ

sxΣ

, xeΣ = xΣ.

For high Q2 the better methods to chose are the e, the DA, and the eΣ. The DA

method has good purity in the full range of x and Q2 but is in general less precise that

the other two, which behave similar at high Q2 and at high and low x. Reference [81]

remarks the weakness of the e method at low y; however the lower limit of y in this

analysis is not so low and the inclusive cross section calculated with e and eΣ gives

the same value, within the systematic errors. The total systematic error for the eΣ

method has a contribution from the determination of the hadronic energy and is of

the same size as the systematic error from the e method. This method has been

chosen for the reconstruction of event kinematics in this work.

132 APPENDIX A. RECONSTRUCTION METHODS

Appendix B

Multiwire proportional and driftchambers

The multiwire proportional chambers (MWPC) were developed by Charpak

and his collaborators at CERN in 1968. It is a particle detector consisting essentially

of a container of gas subjected to an electric field whose operating principle is based in

the collection of electrons and ions left by an incident particle when passing through

the chamber.

A particle passing by a gaseous medium losses energy by elastic scattering, by

excitation and by ionization of the gas atoms. The energy loss of the incident particle

in elastic scattering is generally so small that it does not play a significant role in the

operation of the detector. The excitation process raises the gas atoms or molecules to

an excited energy level which deexcite by photon emission, but the most important

process for the operation is the ionization. This occurs when the energy imparted

to the atoms in the medium exceeds its ionization potential and they liberate one or

more electrons leaving positive ions.

The primary ionization is defined to be the number of ionizing collisions per unit

length suffered by the incident particle. Some of the liberated electrons may still have

sufficient energy to cause more ionization what is called secondary ionization. The

MWPC’s use an electric field in the active region so the charged ionization products

have a net motion in the direction of the field.

133

134 APPENDIX B. MULTIWIRE PROPORTIONAL AND DRIFT CHAMBERS

Figure B.1: a) Typical desing construction and b) electric field configuration of amultiwire proportional chamber.

a) b)

A typical geometry of a MWPC can be seen in Figure B.1a), where a plane of

anodes wires is lying between two cathodes planes. A positive voltage is connected

to the sensing wires while the cathode wires are set to a negative voltage in order

to create an electric field configuration as shown in Figure B.1b). An important

point to take care during the construction is that the wire spacing be very uniform

throughout all the detector because a small displacement of a wire or any irregularity

in their diameters can lead to a large change in the charge provided by the displaced

wire and on adjacent wires.

Due to the voltage applied to the wires, electrostatic forces are present. These

forces can cause a net attraction of the cathode toward the anode plane producing a

curvature in the center varying the gap separation and therefore the gain. Another

effect is the displacement of the wires from the nominal positions if the electrostatic

force on the wires is greater than the tension of the wire.

The filling gas should satisfy the desirable properties, mainly low working voltage,

high gain, good proportionality, high rate capability, long lifetime, high specific ion-

ization, fast recovery and avoid recombination that can damage or contaminate the

chamber electrodes. Usually mixtures of gases are needed to optimize the desirable

features as possible.

When a charged particle passes through the chambers, a primary ionization is

135

produced, the electrons liberated will travel with a known velocity towards the anode

wires inducing secondary collisions or avalanche, which occurs within a few wire

diameters of the anode because of the 1/r electric field dependence. Therefore, the

amount of multiplication is a strong function of the wire diameter. On the other

hand, the wire diameter must not be too small or else it would be incapable of

maintaining the tension necessary to resist the electrostatic forces acting on it.

This avalanche is collected at the chamber electrodes and induces a convenient

current signal along the wires to the external circuit. The output pulse is proportional

to the number of primary ion pairs hence the name of the chamber.

Analysing the detected signal it is possible to reconstruct the trajectory of the

particle using the distribution of sense wires hits and the charge distribution.

Although MWPC have no energy resolution, they are almost 100% efficient for

the detection of single, minimum ionizing particles (MIP), allow a large improvement

in spatial resolution and they also have a good response to many simultaneous tracks

due to the fact that each anode wire is essentially an independent detector.

The drift chambers appear shortly after the MWPC’s. The aspect exploited

by these new chambers is the spatial information obtained by measuring the drift

time of the electrons coming from an ionizing event. For this purpose, a constant

drift velocity is necessary to have a linear relationship between time and distance.

The design is basically the same structure used for a MWPC but in order to get

electric field uniformity, field wires are intercalated between anodes. So, the anode

plane is such that adjacent sense wires are separated by two potential wires. The

field wires are held at a slightly higher potential than the cathode. This configuration

shapes and adjusts the drift field but also does that the chamber volume forms a

Faraday cage screening against external electromagnetic noise.

They are generally easier to operate compared to MWPC’s but much more at-

tention must be given to the field uniformity and is of utmost importance the correct

choice of the fill gas since a precise knowledge of the drift velocity is necessary.

The advantages of the design (besides the already mentioned for the MWPC’s)

136 APPENDIX B. MULTIWIRE PROPORTIONAL AND DRIFT CHAMBERS

are its shorter deadtime and better resolving time, so a drift chamber can be also

used as trigger detector.

Now the trajectory of the particle can be reconstructed using besides the distri-

bution of sense wire hits and the charge distribution, the drift times to the sense

wires. The spatial and time resolutions depend on the anode wire spacing1, and the

uncertainty in the arrival time of a pulse at the logic electronics after the passage of

an ionizing particle.

In several experiments, the location of the MWPCs or drift chambers is in or near

the field of a magnet. In such cases, the path of the drifting electrons and the drift

velocity will be altered by the Lorentz force. So, it is necessary a precise knowledge

of the magnetic field in order to correlate the drift time with position. It may also

be possible to adjust the electric field direction so as to compensate the effects of the

magnetic field.

1It is typically one-half the wire spacing value.

Appendix C

Q and t measurement

All the wires of the CJC, CIZ, and CIP2k (and COP when it was in operation)

are individually read at both ends separately (or combined), the information is used

for the z determination with the help of the signal parameters, the signal time t and

the pulse integral Q.

The analog signal pulse passes through an amplifier connected to the signal wires,

then the amplified signal is carried to the H1 electronic trailer by a coaxial cable

28 m long. There, the signal is digitized by F1001-FADCs1 synchronized to HERA

frequency (104MHz), which means that every 10 ns a digitizations occurs. The

FADC system signals are continuously digitized and stored in the memories. Sixteen

FADC-channels are housed on one F1001-card and up to 16 F1001 cads are housed

in a F1000 crate. In each F1000 front end crate there is a scanner card acting as a

sample controller for the FADCs. Its function is the copy of data from the FADCs,

during this action, the data is compared with programmable thresholds and any

significant transition is recorded in a hit table. The signal pulses gotten in this way

are analysed for the charge and arriving time determination, analysis (Q, t), during

the L4 level of the trigger.

The electrons created by primary ionization in places with approx. the same drift

time arrive all to the signal wire more and less at the same time (the isochrones).

1Fast Analog to Digital Converter.

137

138 APPENDIX C. Q AND T MEASUREMENT

β

wireSignal

Drift way

Drift electrons

Isochrone

Ionizedparticle

A

B

Figure C.1: Isochrones model.

Figure C.1 illustrates it, marked with ’A’. The electrons liberated in ’B’ arrive to the

wire at a different time.

If a charged particles goes through perpendicularly to the drift direction, the

contribution of an isochrone tangent due to the electrons produced by the primary

ionization is maximum. While the β angle (angle between the perpendicular direction

to the drift direction and a trajectory) is larger, less can be depart from a tangential

approximation to an isochrone.

Figure C.2 shows a typical signal pulse after the digitization. The essential infor-

mation for the drift determination comes from those electrons produced in ’A’ which

contribute to the sharp rise of the pulse, while the ones produced in ’B’ arrive later

and belong to the smeared out edge of the pulse. A larger contribution of electrons

from ’B’ mean a flatter pulse.

The (Q, t) analysis consists of several steps. First the FADC data are first lin-

earised, then the pedestal for the signal pulses in the hit memory (threshold) is

determined by the average of the 6 bins before the rise of the signal. The next step

is to put in order both pulses from −z and +z originated by the same primary elec-

trons. If there are two pulses in the same wire close to each other such that they

overlap a standard pulse shape is adjusted to each signal pulses and a substraction

of the pulses is made in both wire ends, improving in this way the resolution of two

139

Signal Amplitud

BA

Integration inteval

Presamples

10% Point

50% Point

Charge

50% line

10% line

Time [10ns]Pedestal

Figure C.2: Example of a pulse signal.

hits.

The method for the arriving time determination is called leading edge algorithm.

For both ends, the 50% point of the signal t50% is determined independenly by a linear

interpolation, which corresponds to the half of the maximum value of the signal smax.

In the same way, it is determined the maximum slope between two digitalizations in

the rise signal region. The line defined is used for the t10% determination in which

a pulse signal of 10% of the maximum amplitud (determined by t50% and smax) is

reached. The time t10% is interpreted as the arriving time of the signal.

The determination of the charges Qz+ and Qz− is gotten by the integration of the

signal pulse. The optimal integral interval must be chosen not too short or an error

in the charge determination will be made, but not too large since the small statistic

induces variations in the pulse fall. The chosen mode consists in an interval of 80

FACD digitizations (80 ns) departing from the t50%.

At the end of the readout, the arriving time tA and the charge Q of both wire

ends for each hit is determined. The values are stored in a data bank to be used for

the reconstruction of the tracks.

140 APPENDIX C. Q AND T MEASUREMENT

Appendix D

Track reconstruction

A charged particle passing through the central tracking detector will describe a

helix trajectory due to the effect of the magnetic field acting over it1. For tracks

reconstruction, a projection in the rφ (or xy) plane is done to get some parame-

ters, which are then combined with the z dimension to have the three-dimensional

reconstructed trajectory of the particle.

In the rφ plane, the track projection is described as function of the curvature κ =

1/R, defined as positive (negative) if the direction of φ is clockwise (anticlockwise);

the closest distance to the origin of the rφ plane, closest distance of approach or dca,

with positive sign if the vector going from the origin to the dca point together with

the trajectory direction form a right-handed system; and the angle between the x

axis and the transverse momentum vector in the dca point, the so called azimuthal

angle φ0. The transverse momentum vector in the dca point is seen in the sz plane

as a straight line starting at a z0 position and forming an angle θ with respect to the

z axis, see Figure D.1.

The helix parameters dca and z0 are defined with respect to nominal position,

the origin (0, 0, 0), but a more appropriate definition would be at the real vertex of

the event (the primary), however this is different for each event.

The κ, dca and φ parameters are obtained by fitting the data hits to a circle using

1The Lorentz force ~F = q( ~E + ~vx ~B).

141

142 APPENDIX D. TRACK RECONSTRUCTION

φ 0

z0|d |ca

R = −|κ|1

x zorigin

track

θ

track

vertexprimary

y s

|d|

Figure D.1: Picture of the track reconstruction with the parameter definition tocharacterize them.

the non-iterative algorithm of Karimaki [82], the equation is in polar coordinates:

1

2κ (r2 + dca2) + (1 + κ dca) r sen(φ − ϕ) − dca = 0,

while θ and z0 are determined by a linear least-squares fit:

zi = z0 + Srφi (dz/dS),

where Srφi is the track length for the point zi in the rφ projection, when Srφ =0 at

dca, and the slope dz/dS is converted to θ by θ = arc tan(1/(dz/dS)).

The reconstruction of tracks is done by a software with a fast version at fourth

trigger level L4, which is efficient for tracks originating from the primary vertex with

momentum greater than 100 MeV/c, and by a standard track finding version more

complete and efficient for all kind of tracks but 10 times slower than the first one.

The fast reconstruction, used for background rejection and fast classification of

events, consists of the determination of the bunch crossing time T0 of the events and

the calculation of the drift time of each hit, the search for tracks elements defined

by three hits (triplets) and, from the triplets, assignation of individual trajectories

to get the track parameters.

The T0 of the event can be gotten from a drift time histogram, as mentioned in

appendix C. The drift time of each hit tA,i, stored in a data bank, can be transduced

143

in position information by si = vdrift(tA,i − T0) where si represents the distance

between the trajectory and the signal wire i, this is the drift distance of the electrons

from the primary ionization, and vdrift being the drift velocity considered as constant.

It is also important to consider the beginning time of each wire t0,i, the drift direction

known by the electric field and the Lorentz angle αLor. The values obtained provide

the new calibration constants which are stored in the H1 database.

The search of track elements start by taking three wires with a distance of two

wires (n − 2, n, n + 2) and trying all pairs of hits. Defining i, k as the hit index,

the drift distances dn are calculated by (dn−2i + dn+2

k )/2 and |dn−2i − dn+2

k |/2, if there

are small differences when it is compared to the measured value dnj (small |dn

j − dn|)then, the index of the hits at the triplet wires are stored as a possible track element

together with their κ and φ values calculated assuming dca ≡ 0. After trying all

different three wire combinations, there is a cluster of hit triplets with their own κ

and φ values; from their coordinates a iterative process is made to fit a circle but

now allowing dca 6= 0 to get a specific track candidate. Those with large |dca| and

κ are rejected.

The standard phase of track reconstruction also searches for track elements by

triplets but now on adjacent wires, so at the end chains of hits are extracted, which

are eventually split into two shorter chains if they are long. The accepted chains

are stored as track elements with parameters from the fit. When the track element

is short, it is merged with the previous ones within the same cells, then with the

neighbouring, within one ring and lastly from both CJC1 and CJC2.

The algorithm of merging start comparing pairs of track elements with similar

helix parameters. If the distance between them suggests that they could belong to

the same track, a χ2 fit is performed (in the rφ plane). In case that one element of

a pair has been used in the construction of a new element, the fit to the modified

element(s) is repeated and rejected eventually. In this way, wrong combinations of

short track elements are avoided with high probability.

Finally the drift length is calculated for all possible wires and for all track elements

144 APPENDIX D. TRACK RECONSTRUCTION

ordered by their length and compared to the measurement to reject incompatible

hits and the fits are repeated but now using the acceptable hits, so the track finding

efficiency is improved.

The energy loss dE/dx for a given track is determined from the mean of single-hit

values 1/√

ki = 1/√

(dE/dx)i, excluding hits which are close to another track.

Appendix E

Breit frame of reference

The DIS kinematic is mainly described by Q2, x, y and W 2 in the laboratory

frame (subsection 1.1.1), but there is another frame also commonly used to study the

dynamics of the hadronic final state in DIS, the Breit Frame [83] (BF). This frame

is special because makes things easier for comparison to results of e+e− colliders,

allowing the test of the universality concept of fragmentation in different processes.

The ep BF is reached when the laboratory frame is Lorentz boosted to the

hadronic center of mass frame, followed by a longitudinal boost along a common

z direction such that the incident virtual photon is space-like (has zero energy, zero

transverse momentum and a z component of momentum −Q). The z direction is

chosen to be, as in laboratory frame, positive in the direction of the incoming proton.

The Figure E.1 presents a illustration of the boost. The advantage of the BF is

the maximal separation of the incoming and outgoing partons in the QPM, the two

regions assigned according to the sign of the momentum in the z axis of the BF, pz.

The current hemisphere if pz < 0 and the target hemisphere if pz > 0.

The current region is dominated by the fragments of the struck quark alone

which makes it analogous to the single hemisphere of e+e− → qq annihilation.

The proton remnants go entirely into the target hemisphere. The incoming quark

have four-momentum (Q/2,0,0,Q/2), after the scattering the four-momentum is

(Q/2,0,0,−Q/2), so the maximum momentum a particle can have in current region

145

146 APPENDIX E. BREIT FRAME OF REFERENCE

q=(0,0,0,−Q) e

− Q / 2

q

P

+ Q / 2

q

_e’

z

Figure E.1: Breit frame scheme with the separation in current and target hemi-spheres.

is Q/2 while the target region with much higher momentum can reach a maximum

of Q(1 − x)/2x. The two regions are then asymmetric, particularly at low x, where

the target region occupies most of the available phase space. The central detector in

H1 provides excellent acceptance for the current region studies.

In e+e− annihilation, the two quarks are produced with equal and opposite mo-

menta (±√

see/2) and the scaled hadron momentum is xp = 2phadron/E∗, with E∗

being its center of mass energy. The fragmentation of the quarks in e+e− interactions

can be compared to that in the current region where the scaled momentum spectra

of the particles is then expressed in terms of xp = 2phadrons/Q (considering only

hadrons in the current hemisphere), the Q dependence is similar to that in e+e− at

energy√

see = Q and, as can be easily seen, E∗ is equivalent to Q.

The BF also enables the study of low pT tracks1 since low momenta tracks in the

laboratory frame can occasionally be boosted to higher momenta in the BF. In these

frames the pT arising from the electroweak recoil of the hadronic system against the

scattered lepton is removed, facilitating the observation of QCD effects.

The consideration of higher order processes can, however, affect the QPM in BF,

for instance the BGF and initial state QCDc contribute to the ep cross section but

1In the laboratory frame of reference, low pT tracks have poor acceptance and are removed below150 MeV/c to improve the simulation efficiency.

147

they are not present (and have no analogue) in e+e− annihilation. These processes,

together with final state QCDc (which does occur in hadronic e+e− collisions) can

de-populate the BF current region, even leading to a current hemisphere which is

empty, for further explanation go to reference [84]. Empty current hemisphere events

are included in this analysis for normalisation purposes.

148 APPENDIX E. BREIT FRAME OF REFERENCE

Appendix F

Fits to mass distributions

149

150A

PP

EN

DIX

F.

FIT

ST

OM

ASS

DIS

TR

IBU

TIO

NS

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

/ ndf 2χ 101 / 109

Prob 0.6963

N 20931± 4.949e+05

m 0.0002± 0.4967

σ 0.000238± 0.008507

ν 0.325± 2.031

0

p 38.2± 52.7

1p 0.1024± 0.3388

2p 4.97± 35.57

3

p 13.93± -67.77

4p 11.34± 37.38

HERA II/NDF ~ 0.9261632χ

0.000190±mass = 0.496702

0.000238± = 0.008507σ 305±) in range = 4200

s

0 N(K

S/B = 5.940089

Range = [0.345000,0.700000]

Bin 1

/ ndf 2χ 101 / 109

Prob 0.6963

N 20931± 4.949e+05

m 0.0002± 0.4967

σ 0.000238± 0.008507

ν 0.325± 2.031

0

p 38.2± 52.7

1p 0.1024± 0.3388

2p 4.97± 35.57

3

p 13.93± -67.77

4p 11.34± 37.38

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

/ ndf 2χ 101 / 109

Prob 0.6963

N 20931± 4.949e+05

m 0.0002± 0.4967

σ 0.000238± 0.008507

ν 0.325± 2.031

0

p 38.2± 52.7

1p 0.1024± 0.3388

2p 4.97± 35.57

3

p 13.93± -67.77

4p 11.34± 37.38


0.000190±mass = 0.496702

0.000238± = 0.008507σ 305±) in range = 4200

s

0 N(K

S/B = 5.940089

Range = [0.345000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 95.47 / 109

Prob 0.8189

N 26275± 7.46e+05

m 0.0002± 0.4967

σ 0.000192± 0.008419

ν 0.296± 2.097

0

p 55.1± 111.1

1p 0.0700± 0.4319

2p 4.21± 37.05

3

p 11.51± -70.88

4p 9.25± 38.18


0.000162±mass = 0.496729

0.000192± = 0.008419σ 374±) in range = 6269

s

0 N(K

S/B = 4.719892

Range = [0.345000,0.700000]

Bin 2

/ ndf 2χ 95.47 / 109

Prob 0.8189

N 26275± 7.46e+05

m 0.0002± 0.4967

σ 0.000192± 0.008419

ν 0.296± 2.097

0

p 55.1± 111.1

1p 0.0700± 0.4319

2p 4.21± 37.05

3

p 11.51± -70.88

4p 9.25± 38.18

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 95.47 / 109

Prob 0.8189

N 26275± 7.46e+05

m 0.0002± 0.4967

σ 0.000192± 0.008419

ν 0.296± 2.097

0

p 55.1± 111.1

1p 0.0700± 0.4319

2p 4.21± 37.05

3

p 11.51± -70.88

4p 9.25± 38.18


0.000162±mass = 0.496729

0.000192± = 0.008419σ 374±) in range = 6269

s

0 N(K

S/B = 4.719892

Range = [0.345000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

/ ndf 2χ 107.4 / 110

Prob 0.5516

N 41781± 1.158e+06

m 0.000± 0.497

σ 0.000189± 0.008931

ν 0.158± 1.326

0

p 13.0± 154.2

1p 0.0542± 0.3765

2p 2.33± 37.78

3

p 8.49± -76.55

4p 7.53± 45.23


0.000139±mass = 0.496967

0.000189± = 0.008931σ 637±) in range = 10197

s

0 N(K

S/B = 5.682566

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 107.4 / 110

Prob 0.5516

N 41781± 1.158e+06

m 0.000± 0.497

σ 0.000189± 0.008931

ν 0.158± 1.326

0

p 13.0± 154.2

1p 0.0542± 0.3765

2p 2.33± 37.78

3

p 8.49± -76.55

4p 7.53± 45.23

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

/ ndf 2χ 107.4 / 110

Prob 0.5516

N 41781± 1.158e+06

m 0.000± 0.497

σ 0.000189± 0.008931

ν 0.158± 1.326

0

p 13.0± 154.2

1p 0.0542± 0.3765

2p 2.33± 37.78

3

p 8.49± -76.55

4p 7.53± 45.23


0.000139±mass = 0.496967

0.000189± = 0.008931σ 637±) in range = 10197

s

0 N(K

S/B = 5.682566

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

/ ndf 2χ 114.3 / 110

Prob 0.3713

N 44591± 1.198e+06

m 0.0001± 0.4971

σ 0.000182± 0.008788

ν 0.150± 1.245

0

p 47.5± 139.9

1p 0.0466± 0.3531

2p 2.61± 36.99

3

p 7.69± -71.99

4p 6.56± 40.94


0.000134±mass = 0.497129

0.000182± = 0.008788σ 663±) in range = 10352

s

0 N(K

S/B = 4.953475

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 114.3 / 110

Prob 0.3713

N 44591± 1.198e+06

m 0.0001± 0.4971

σ 0.000182± 0.008788

ν 0.150± 1.245

0

p 47.5± 139.9

1p 0.0466± 0.3531

2p 2.61± 36.99

3

p 7.69± -71.99

4p 6.56± 40.94

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

/ ndf 2χ 114.3 / 110

Prob 0.3713

N 44591± 1.198e+06

m 0.0001± 0.4971

σ 0.000182± 0.008788

ν 0.150± 1.245

0

p 47.5± 139.9

1p 0.0466± 0.3531

2p 2.61± 36.99

3

p 7.69± -71.99

4p 6.56± 40.94


0.000134±mass = 0.497129

0.000182± = 0.008788σ 663±) in range = 10352

s

0 N(K

S/B = 4.953475

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

/ ndf 2χ 124.3 / 110

Prob 0.166

N 34214± 5.34e+05

m 0.0002± 0.4973 σ 0.0003± 0.0102 ν 0.250± 1.186

0p 59.1± 136.4

1

p 0.0604± 0.3943

2p 4.19± 35.82

3

p 12.38± -72.94

4p 10.44± 43.46


0.000233±mass = 0.497280

0.000339± = 0.010203σ 588±) in range = 5322

s

0 N(K

S/B = 4.574761

Range = [0.344000,0.700000]

Bin 5

/ ndf 2χ 124.3 / 110

Prob 0.166

N 34214± 5.34e+05

m 0.0002± 0.4973 σ 0.0003± 0.0102 ν 0.250± 1.186

0p 59.1± 136.4

1

p 0.0604± 0.3943

2p 4.19± 35.82

3

p 12.38± -72.94

4p 10.44± 43.46

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

/ ndf 2χ 124.3 / 110

Prob 0.166

N 34214± 5.34e+05

m 0.0002± 0.4973 σ 0.0003± 0.0102 ν 0.250± 1.186

0p 59.1± 136.4

1

p 0.0604± 0.3943

2p 4.19± 35.82

3

p 12.38± -72.94

4p 10.44± 43.46


0.000233±mass = 0.497280

0.000339± = 0.010203σ 588±) in range = 5322

s

0 N(K

S/B = 4.574761

Range = [0.344000,0.700000]

Bin 5

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

/ ndf 2χ 107.5 / 110

Prob 0.5507

N 28528± 3.363e+05

m 0.0003± 0.4971 σ 0.00083± 0.00992 ν 0.0528± 0.3982

0p 1.035± 3.371

1

p 0.0858± 0.6073

2p 3.72± 61.91

3

p 11.5± -129.5

4p 9.67± 81.93


0.000322±mass = 0.497150

0.000834± = 0.009920σ 568±) in range = 2630

s

0 N(K

S/B = 2.981262

Range = [0.344000,0.700000]

Bin 6

Figu

reF.1:

Fits

toth

ein

variant

mass

distrib

ution

fromdata

inbin

sof

Q2.

151

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800 / ndf 2χ 91.82 / 110

Prob 0.8952

N 23504± 6.497e+05

m 0.0002± 0.4966

σ 0.000201± 0.008311

ν 0.320± 2.238

0

p 13.37± 19.86

1p 0.0651± 0.4251

2p 4.97± 46.53

3

p 12.54± -91.24

4p 9.84± 52.65


0.000167±mass = 0.496568

0.000201± = 0.008311σ 334±) in range = 5392

s

0 N(K

S/B = 5.230564

Range = [0.344000,0.700000]

Bin 1

/ ndf 2χ 91.82 / 110

Prob 0.8952

N 23504± 6.497e+05

m 0.0002± 0.4966

σ 0.000201± 0.008311

ν 0.320± 2.238

0

p 13.37± 19.86

1p 0.0651± 0.4251

2p 4.97± 46.53

3

p 12.54± -91.24

4p 9.84± 52.65

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800 / ndf 2χ 91.82 / 110

Prob 0.8952

N 23504± 6.497e+05

m 0.0002± 0.4966

σ 0.000201± 0.008311

ν 0.320± 2.238

0

p 13.37± 19.86

1p 0.0651± 0.4251

2p 4.97± 46.53

3

p 12.54± -91.24

4p 9.84± 52.65


0.000167±mass = 0.496568

0.000201± = 0.008311σ 334±) in range = 5392

s

0 N(K

S/B = 5.230564

Range = [0.344000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

200

400

600

800

1000

1200

1400

1600

1800

/ ndf 2χ 129.2 / 109

Prob 0.09069

N 47804± 1.745e+06

m 0.0001± 0.4969

σ 0.000138± 0.008621

ν 0.151± 1.558

0

p 61.1± 120.3

1p 0.0495± 0.3456

2p 3.62± 38.39

3

p 9.07± -72.18

4p 7.06± 39.36


0.000109±mass = 0.496927

0.000138± = 0.008621σ 688±) in range = 14936

s

0 N(K

S/B = 5.298865

Range = [0.345000,0.700000]

Bin 2

/ ndf 2χ 129.2 / 109

Prob 0.09069

N 47804± 1.745e+06

m 0.0001± 0.4969

σ 0.000138± 0.008621

ν 0.151± 1.558

0

p 61.1± 120.3

1p 0.0495± 0.3456

2p 3.62± 38.39

3

p 9.07± -72.18

4p 7.06± 39.36

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

200

400

600

800

1000

1200

1400

1600

1800

/ ndf 2χ 129.2 / 109

Prob 0.09069

N 47804± 1.745e+06

m 0.0001± 0.4969

σ 0.000138± 0.008621

ν 0.151± 1.558

0

p 61.1± 120.3

1p 0.0495± 0.3456

2p 3.62± 38.39

3

p 9.07± -72.18

4p 7.06± 39.36


0.000109±mass = 0.496927

0.000138± = 0.008621σ 688±) in range = 14936

s

0 N(K

S/B = 5.298865

Range = [0.345000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

/ ndf 2χ 109.5 / 109

Prob 0.4679

N 55420± 1.435e+06

m 0.0001± 0.4972

σ 0.000183± 0.009121

ν 0.130± 1.057

0

p 44.3± 125

1p 0.0559± 0.3304

2p 2.73± 39.67

3

p 8.29± -80.77

4p 7.05± 48.93


0.000133±mass = 0.497189

0.000183± = 0.009121σ 865±) in range = 12712

s

0 N(K

S/B = 5.520706

Range = [0.345000,0.700000]

Bin 3

/ ndf 2χ 109.5 / 109

Prob 0.4679

N 55420± 1.435e+06

m 0.0001± 0.4972

σ 0.000183± 0.009121

ν 0.130± 1.057

0

p 44.3± 125

1p 0.0559± 0.3304

2p 2.73± 39.67

3

p 8.29± -80.77

4p 7.05± 48.93

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

/ ndf 2χ 109.5 / 109

Prob 0.4679

N 55420± 1.435e+06

m 0.0001± 0.4972

σ 0.000183± 0.009121

ν 0.130± 1.057

0

p 44.3± 125

1p 0.0559± 0.3304

2p 2.73± 39.67

3

p 8.29± -80.77

4p 7.05± 48.93


0.000133±mass = 0.497189

0.000183± = 0.009121σ 865±) in range = 12712

s

0 N(K

S/B = 5.520706

Range = [0.345000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 133 / 110

Prob 0.06667

N 30762± 5.372e+05

m 0.0002± 0.4972 σ 0.00032± 0.01017 ν 0.36± 1.62

0p 1.38± 12.45

1

p 0.0465± 0.4462

2p 1.90± 52.34

3

p 6.9± -100.9

4p 6.12± 58.28


0.000239±mass = 0.497165

0.000323± = 0.010167σ 517±) in range = 5417

s

0 N(K

S/B = 2.551003

Range = [0.344000,0.700000]

Bin 4

Figu

reF.2:

Fits

toth

ein

variant

mass

distrib

ution

fromdata

inbin

sof

x.

152A

PP

EN

DIX

F.

FIT

ST

OM

ASS

DIS

TR

IBU

TIO

NS

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 89.31 / 110

Prob 0.9262

N 31050± 7.97e+05

m 0.0002± 0.4964

σ 0.000197± 0.008263

ν 0.24± 1.81

0

p 1.48± 15.86

1p 0.0787± 0.4408

2p 3.52± 48.44

3

p 12.48± -95.52

4p 10.97± 54.92


0.000156±mass = 0.496388

0.000197± = 0.008263σ 428±) in range = 6561

s

0 N(K

S/B = 6.846985

Range = [0.344000,0.700000]

Bin 1

/ ndf 2χ 89.31 / 110

Prob 0.9262

N 31050± 7.97e+05

m 0.0002± 0.4964

σ 0.000197± 0.008263

ν 0.24± 1.81

0

p 1.48± 15.86

1p 0.0787± 0.4408

2p 3.52± 48.44

3

p 12.48± -95.52

4p 10.97± 54.92

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 89.31 / 110

Prob 0.9262

N 31050± 7.97e+05

m 0.0002± 0.4964

σ 0.000197± 0.008263

ν 0.24± 1.81

0

p 1.48± 15.86

1p 0.0787± 0.4408

2p 3.52± 48.44

3

p 12.48± -95.52

4p 10.97± 54.92


0.000156±mass = 0.496388

0.000197± = 0.008263σ 428±) in range = 6561

s

0 N(K

S/B = 6.846985

Range = [0.344000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 113.9 / 108

Prob 0.3297

N 51351± 1.041e+06

m 0.0002± 0.4967

σ 0.000216± 0.008904

ν 0.136± 0.932

0

p 3.34± 35.81

1p 0.1191± 0.4439

2p 4.58± 43.78

3

p 14.9± -88.6

4p 12.4± 53.4


0.000151±mass = 0.496659

0.000216± = 0.008904σ 783±) in range = 8901

s

0 N(K

S/B = 8.569452

Range = [0.350000,0.700000]

Bin 2

/ ndf 2χ 113.9 / 108

Prob 0.3297

N 51351± 1.041e+06

m 0.0002± 0.4967

σ 0.000216± 0.008904

ν 0.136± 0.932

0

p 3.34± 35.81

1p 0.1191± 0.4439

2p 4.58± 43.78

3

p 14.9± -88.6

4p 12.4± 53.4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 113.9 / 108

Prob 0.3297

N 51351± 1.041e+06

m 0.0002± 0.4967

σ 0.000216± 0.008904

ν 0.136± 0.932

0

p 3.34± 35.81

1p 0.1191± 0.4439

2p 4.58± 43.78

3

p 14.9± -88.6

4p 12.4± 53.4


0.000151±mass = 0.496659

0.000216± = 0.008904σ 783±) in range = 8901

s

0 N(K

S/B = 8.569452

Range = [0.350000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000 / ndf 2χ 94.47 / 104

Prob 0.7376

N 49579± 1.005e+06

m 0.000± 0.497

σ 0.000232± 0.009305

ν 0.1482± 0.9693

0

p 7.274± 8.607

1p 0.15923± -0.07678

2p 5.58± 36.27

3

p 15.37± -57.95

4p 12.10± 27.62


0.000160±mass = 0.496962

0.000232± = 0.009305σ 798±) in range = 8982

s

0 N(K

S/B = 6.899873

Range = [0.360000,0.700000]

Bin 3

/ ndf 2χ 94.47 / 104

Prob 0.7376

N 49579± 1.005e+06

m 0.000± 0.497

σ 0.000232± 0.009305

ν 0.1482± 0.9693

0

p 7.274± 8.607

1p 0.15923± -0.07678

2p 5.58± 36.27

3

p 15.37± -57.95

4p 12.10± 27.62

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000 / ndf 2χ 94.47 / 104

Prob 0.7376

N 49579± 1.005e+06

m 0.000± 0.497

σ 0.000232± 0.009305

ν 0.1482± 0.9693

0

p 7.274± 8.607

1p 0.15923± -0.07678

2p 5.58± 36.27

3

p 15.37± -57.95

4p 12.10± 27.62


0.000160±mass = 0.496962

0.000232± = 0.009305σ 798±) in range = 8982

s

0 N(K

S/B = 6.899873

Range = [0.360000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 154.6 / 110

Prob 0.003296

N 40108± 1.001e+06

m 0.0002± 0.4972

σ 0.000183± 0.008361

ν 0.163± 1.545

0

p 2.06± 27.48

1p 0.0431± 0.3044

2p 2.07± 43.76

3

p 7.61± -81.06

4p 6.8± 44.5


0.000151±mass = 0.497151

0.000183± = 0.008361σ 542±) in range = 8309

s

0 N(K

S/B = 3.963126

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 154.6 / 110

Prob 0.003296

N 40108± 1.001e+06

m 0.0002± 0.4972

σ 0.000183± 0.008361

ν 0.163± 1.545

0

p 2.06± 27.48

1p 0.0431± 0.3044

2p 2.07± 43.76

3

p 7.61± -81.06

4p 6.8± 44.5

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 154.6 / 110

Prob 0.003296

N 40108± 1.001e+06

m 0.0002± 0.4972

σ 0.000183± 0.008361

ν 0.163± 1.545

0

p 2.06± 27.48

1p 0.0431± 0.3044

2p 2.07± 43.76

3

p 7.61± -81.06

4p 6.8± 44.5


0.000151±mass = 0.497151

0.000183± = 0.008361σ 542±) in range = 8309

s

0 N(K

S/B = 3.963126

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800 / ndf 2χ 137.4 / 109

Prob 0.03417

N 24721± 6.078e+05

m 0.0002± 0.4979 σ 0.00026± 0.01005 ν 0.545± 2.678

0p 17.30± 50.23

1

p 0.0509± 0.3817

2p 2.97± 44.93

3

p 8.04± -87.61

4p 6.37± 51.12


0.000206±mass = 0.497889

0.000262± = 0.010050σ 416±) in range = 6103

s

0 N(K

S/B = 2.348214

Range = [0.345000,0.700000]

Bin 5

Figu

reF.3:

Fits

toth

ein

variant

mass

distrib

ution

fromdata

inbin

sof

η.

153

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 129.5 / 101

Prob 0.02963

N 29105± 8.351e+05

m 0.0001± 0.4967

σ 0.000179± 0.007051

ν 0.545± 3.118

0

p 15.93± 34.42

1p 0.0891± 0.1473

2p 3.98± 48.86

3

p 10.33± -98.01

4p 7.76± 58.32


0.000144±mass = 0.496704

0.000179± = 0.007051σ 360±) in range = 5887

s

0 N(K

S/B = 1.642742

Range = [0.370000,0.700000]

Bin 1

/ ndf 2χ 129.5 / 101

Prob 0.02963

N 29105± 8.351e+05

m 0.0001± 0.4967

σ 0.000179± 0.007051

ν 0.545± 3.118

0

p 15.93± 34.42

1p 0.0891± 0.1473

2p 3.98± 48.86

3

p 10.33± -98.01

4p 7.76± 58.32

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 129.5 / 101

Prob 0.02963

N 29105± 8.351e+05

m 0.0001± 0.4967

σ 0.000179± 0.007051

ν 0.545± 3.118

0

p 15.93± 34.42

1p 0.0891± 0.1473

2p 3.98± 48.86

3

p 10.33± -98.01

4p 7.76± 58.32


0.000144±mass = 0.496704

0.000179± = 0.007051σ 360±) in range = 5887

s

0 N(K

S/B = 1.642742

Range = [0.370000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 108.7 / 110

Prob 0.5159

N 24612± 7.134e+05

m 0.000± 0.497

σ 0.000189± 0.007539

ν 0.468± 3.041

0

p 1.9± 26

1p 0.0767± 0.4527

2p 3.00± 45.98

3

p 9.81± -90.33

4p 8.15± 53.07


0.000148±mass = 0.497012

0.000189± = 0.007539σ 325±) in range = 5377

s

0 N(K

S/B = 4.232534

Range = [0.344000,0.700000]

Bin 2

/ ndf 2χ 108.7 / 110

Prob 0.5159

N 24612± 7.134e+05

m 0.000± 0.497

σ 0.000189± 0.007539

ν 0.468± 3.041

0

p 1.9± 26

1p 0.0767± 0.4527

2p 3.00± 45.98

3

p 9.81± -90.33

4p 8.15± 53.07

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 108.7 / 110

Prob 0.5159

N 24612± 7.134e+05

m 0.000± 0.497

σ 0.000189± 0.007539

ν 0.468± 3.041

0

p 1.9± 26

1p 0.0767± 0.4527

2p 3.00± 45.98

3

p 9.81± -90.33

4p 8.15± 53.07


0.000148±mass = 0.497012

0.000189± = 0.007539σ 325±) in range = 5377

s

0 N(K

S/B = 4.232534

Range = [0.344000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 124 / 110

Prob 0.1713

N 26281± 8.216e+05

m 0.0002± 0.4968

σ 0.000190± 0.008883

ν 0.213± 1.898

0

p 124.5± 253.3

1p 0.0669± 0.3005

2p 3.3± 23.7

3

p 9.77± -42.16

4p 8.44± 21.96


0.000159±mass = 0.496778

0.000190± = 0.008883σ 402±) in range = 7273

s

0 N(K

S/B = 8.535026

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 124 / 110

Prob 0.1713

N 26281± 8.216e+05

m 0.0002± 0.4968

σ 0.000190± 0.008883

ν 0.213± 1.898

0

p 124.5± 253.3

1p 0.0669± 0.3005

2p 3.3± 23.7

3

p 9.77± -42.16

4p 8.44± 21.96

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 124 / 110

Prob 0.1713

N 26281± 8.216e+05

m 0.0002± 0.4968

σ 0.000190± 0.008883

ν 0.213± 1.898

0

p 124.5± 253.3

1p 0.0669± 0.3005

2p 3.3± 23.7

3

p 9.77± -42.16

4p 8.44± 21.96


0.000159±mass = 0.496778

0.000190± = 0.008883σ 402±) in range = 7273

s

0 N(K

S/B = 8.535026

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900

/ ndf 2χ 98.67 / 110

Prob 0.7722

N 31697± 8.439e+05

m 0.000± 0.497

σ 0.000219± 0.009493

ν 0.131± 1.195

0

p 4.2± 25.8

1p 0.1796± 0.6982

2p 5.86± 44.75

3

p 18.13± -91.14

4p 14.37± 56.66


0.000166±mass = 0.497041

0.000219± = 0.009493σ 528±) in range = 7846

s

0 N(K

S/B = 13.326587

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 98.67 / 110

Prob 0.7722

N 31697± 8.439e+05

m 0.000± 0.497

σ 0.000219± 0.009493

ν 0.131± 1.195

0

p 4.2± 25.8

1p 0.1796± 0.6982

2p 5.86± 44.75

3

p 18.13± -91.14

4p 14.37± 56.66

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900

/ ndf 2χ 98.67 / 110

Prob 0.7722

N 31697± 8.439e+05

m 0.000± 0.497

σ 0.000219± 0.009493

ν 0.131± 1.195

0

p 4.2± 25.8

1p 0.1796± 0.6982

2p 5.86± 44.75

3

p 18.13± -91.14

4p 14.37± 56.66


0.000166±mass = 0.497041

0.000219± = 0.009493σ 528±) in range = 7846

s

0 N(K

S/B = 13.326587

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 105.7 / 109

Prob 0.5715

N 28855± 6.692e+05

m 0.0002± 0.4972 σ 0.00031± 0.01199 ν 0.132± 1.039

0p 14.41± 40.82

1

p 0.587± 1.475

2p 15.4± 53.8

3

p 43.9± -112.3

4p 32.28± 68.83


0.000213±mass = 0.497214

0.000306± = 0.011988σ 623±) in range = 7703

s

0 N(K

S/B = 15.976900

Range = [0.344000,0.700000]

Bin 5

/ ndf 2χ 105.7 / 109

Prob 0.5715

N 28855± 6.692e+05

m 0.0002± 0.4972 σ 0.00031± 0.01199 ν 0.132± 1.039

0p 14.41± 40.82

1

p 0.587± 1.475

2p 15.4± 53.8

3

p 43.9± -112.3

4p 32.28± 68.83

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 105.7 / 109

Prob 0.5715

N 28855± 6.692e+05

m 0.0002± 0.4972 σ 0.00031± 0.01199 ν 0.132± 1.039

0p 14.41± 40.82

1

p 0.587± 1.475

2p 15.4± 53.8

3

p 43.9± -112.3

4p 32.28± 68.83


0.000213±mass = 0.497214

0.000306± = 0.011988σ 623±) in range = 7703

s

0 N(K

S/B = 15.976900

Range = [0.344000,0.700000]

Bin 5

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV0

50

100

150

200

250

300

350

400

450 / ndf 2χ 151.3 / 110

Prob 0.005525

N 17744± 3.608e+05

m 0.0003± 0.4979 σ 0.00059± 0.01393 ν 0.16± 1.11

0p 3.569± 5.041

1

p 0.737± 2.141

2p 22.08± 77.05

3

p 58.1± -146

4p 41.27± 76.16


0.000341±mass = 0.497895

0.000592± = 0.013934σ 508±) in range = 4829

s

0 N(K

S/B = 4.612215

Range = [0.344000,0.700000]

Bin 6

Figu

reF.4:

Fits

toth

ein

variant

mass

distrib

ution

fromdata

inbin

sof

pT.

154A

PP

EN

DIX

F.

FIT

ST

OM

ASS

DIS

TR

IBU

TIO

NS

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

/ ndf 2χ 108.5 / 104

Prob 0.363

N 27511± 5.164e+05

m 0.0002± 0.4967

σ 0.000263± 0.007847

ν 0.397± 1.897

0

p 15.10± 29.89

1p 0.099± 0.224

2p 4.59± 47.35

3

p 12.41± -96.82

4p 9.62± 58.86


0.000205±mass = 0.496738

0.000263± = 0.007847σ 365±) in range = 4039

s

0 N(K

S/B = 2.176749

Range = [0.360000,0.700000]

Bin 1

/ ndf 2χ 108.5 / 104

Prob 0.363

N 27511± 5.164e+05

m 0.0002± 0.4967

σ 0.000263± 0.007847

ν 0.397± 1.897

0

p 15.10± 29.89

1p 0.099± 0.224

2p 4.59± 47.35

3

p 12.41± -96.82

4p 9.62± 58.86

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

/ ndf 2χ 108.5 / 104

Prob 0.363

N 27511± 5.164e+05

m 0.0002± 0.4967

σ 0.000263± 0.007847

ν 0.397± 1.897

0

p 15.10± 29.89

1p 0.099± 0.224

2p 4.59± 47.35

3

p 12.41± -96.82

4p 9.62± 58.86


0.000205±mass = 0.496738

0.000263± = 0.007847σ 365±) in range = 4039

s

0 N(K

S/B = 2.176749

Range = [0.360000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

/ ndf 2χ 112.6 / 110

Prob 0.4124

N 33991± 8.028e+05

m 0.0002± 0.4965

σ 0.000212± 0.008478

ν 0.140± 1.124

0

p 6.64± 55.83

1p 0.1144± 0.6223

2p 4.19± 43.49

3

p 13.85± -91.24

4p 11.59± 56.86


0.000165±mass = 0.496538

0.000212± = 0.008478σ 502±) in range = 6656

s

0 N(K

S/B = 8.490764

Range = [0.344000,0.700000]

Bin 2

/ ndf 2χ 112.6 / 110

Prob 0.4124

N 33991± 8.028e+05

m 0.0002± 0.4965

σ 0.000212± 0.008478

ν 0.140± 1.124

0

p 6.64± 55.83

1p 0.1144± 0.6223

2p 4.19± 43.49

3

p 13.85± -91.24

4p 11.59± 56.86

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

/ ndf 2χ 112.6 / 110

Prob 0.4124

N 33991± 8.028e+05

m 0.0002± 0.4965

σ 0.000212± 0.008478

ν 0.140± 1.124

0

p 6.64± 55.83

1p 0.1144± 0.6223

2p 4.19± 43.49

3

p 13.85± -91.24

4p 11.59± 56.86


0.000165±mass = 0.496538

0.000212± = 0.008478σ 502±) in range = 6656

s

0 N(K

S/B = 8.490764

Range = [0.344000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

/ ndf 2χ 96.31 / 110

Prob 0.8209

N 27154± 5.368e+05

m 0.0002± 0.4963

σ 0.00032± 0.01006 ν 0.154± 1.048

0p 5.32± 16.19

1

p 0.552± 1.344

2p 16.08± 56.71

3

p 46.5± -113.6

4p 34.77± 64.58


0.000219±mass = 0.496299

0.000317± = 0.010063σ 494±) in range = 5227

s

0 N(K

S/B = 12.040656

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 96.31 / 110

Prob 0.8209

N 27154± 5.368e+05

m 0.0002± 0.4963

σ 0.00032± 0.01006 ν 0.154± 1.048

0p 5.32± 16.19

1

p 0.552± 1.344

2p 16.08± 56.71

3

p 46.5± -113.6

4p 34.77± 64.58

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

/ ndf 2χ 96.31 / 110

Prob 0.8209

N 27154± 5.368e+05

m 0.0002± 0.4963

σ 0.00032± 0.01006 ν 0.154± 1.048

0p 5.32± 16.19

1

p 0.552± 1.344

2p 16.08± 56.71

3

p 46.5± -113.6

4p 34.77± 64.58


0.000219±mass = 0.496299

0.000317± = 0.010063σ 494±) in range = 5227

s

0 N(K

S/B = 12.040656

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

400

450 / ndf 2χ 113.8 / 107

Prob 0.3074

N 12216± 4.162e+05

m 0.0003± 0.4974 σ 0.00042± 0.01108 ν 0.1± 1

0p 24.54± 54.11

1

p 1.194± 2.707

2p 32.61± 77.69

3

p 89.7± -168.7

4p 64.40± 99.91


0.000260±mass = 0.497417

0.000424± = 0.011081σ 356±) in range = 4425

s

0 N(K

S/B = 12.365727

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 113.8 / 107

Prob 0.3074

N 12216± 4.162e+05

m 0.0003± 0.4974 σ 0.00042± 0.01108 ν 0.1± 1

0p 24.54± 54.11

1

p 1.194± 2.707

2p 32.61± 77.69

3

p 89.7± -168.7

4p 64.40± 99.91

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

400

450 / ndf 2χ 113.8 / 107

Prob 0.3074

N 12216± 4.162e+05

m 0.0003± 0.4974 σ 0.00042± 0.01108 ν 0.1± 1

0p 24.54± 54.11

1

p 1.194± 2.707

2p 32.61± 77.69

3

p 89.7± -168.7

4p 64.40± 99.91


0.000260±mass = 0.497417

0.000424± = 0.011081σ 356±) in range = 4425

s

0 N(K

S/B = 12.365727

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

20

40

60

80

100

120

140

160

180 / ndf 2χ 104.5 / 103

Prob 0.4401

N 7215± 1.562e+05

m 0.0005± 0.4971 σ 0.00063± 0.01407 ν 0.1± 1

0p 52.19± 99.84

1

p 17.23± 30.13

2p 329.8± 621.2

3

p 792.4± -1486

4p 510.3± 953


0.000545±mass = 0.497076

0.000632± = 0.014068σ 206±) in range = 2085

s

0 N(K

S/B = 18.712476

Range = [0.344000,0.700000]

Bin 5

Figu

reF.5:

Fits

toth

ein

variant

mass

distrib

ution

fromdata

inbin

sof

xC

BF

pfor

the

curren

them

isphere

inth

eB

reitFram

e.

155

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

/ ndf 2χ 141.3 / 104

Prob 0.008742

N 24286± 2.632e+05

m 0.0003± 0.4972

σ 0.000376± 0.007123

ν 0.448± 1.394

0

p 14.92± 15.62

1p 0.1313± 0.1598

2p 6.83± 48.41

3

p 17.2± -101.5

4p 13.06± 63.47


0.000284±mass = 0.497151

0.000376± = 0.007123σ 291±) in range = 1857

s

0 N(K

S/B = 1.790885

Range = [0.360000,0.700000]

Bin 1

/ ndf 2χ 141.3 / 104

Prob 0.008742

N 24286± 2.632e+05

m 0.0003± 0.4972

σ 0.000376± 0.007123

ν 0.448± 1.394

0

p 14.92± 15.62

1p 0.1313± 0.1598

2p 6.83± 48.41

3

p 17.2± -101.5

4p 13.06± 63.47

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

/ ndf 2χ 141.3 / 104

Prob 0.008742

N 24286± 2.632e+05

m 0.0003± 0.4972

σ 0.000376± 0.007123

ν 0.448± 1.394

0

p 14.92± 15.62

1p 0.1313± 0.1598

2p 6.83± 48.41

3

p 17.2± -101.5

4p 13.06± 63.47


0.000284±mass = 0.497151

0.000376± = 0.007123σ 291±) in range = 1857

s

0 N(K

S/B = 1.790885

Range = [0.360000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

100

200

300

400

500

/ ndf 2χ 128 / 109

Prob 0.103

N 15569± 4.173e+05

m 0.0002± 0.4969

σ 0.000220± 0.007777

ν 0.384± 3.485

0

p 0.0112± 0.0528

1p 0.0539± 0.2959

2p 2.54± 80.37

3

p 7.7± -156.7

4p 6.31± 94.35


0.000211±mass = 0.496889

0.000220± = 0.007777σ 216±) in range = 3245

s

0 N(K

S/B = 2.934986

Range = [0.345000,0.700000]

Bin 2

/ ndf 2χ 128 / 109

Prob 0.103

N 15569± 4.173e+05

m 0.0002± 0.4969

σ 0.000220± 0.007777

ν 0.384± 3.485

0

p 0.0112± 0.0528

1p 0.0539± 0.2959

2p 2.54± 80.37

3

p 7.7± -156.7

4p 6.31± 94.35

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

100

200

300

400

500

/ ndf 2χ 128 / 109

Prob 0.103

N 15569± 4.173e+05

m 0.0002± 0.4969

σ 0.000220± 0.007777

ν 0.384± 3.485

0

p 0.0112± 0.0528

1p 0.0539± 0.2959

2p 2.54± 80.37

3

p 7.7± -156.7

4p 6.31± 94.35


0.000211±mass = 0.496889

0.000220± = 0.007777σ 216±) in range = 3245

s

0 N(K

S/B = 2.934986

Range = [0.345000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500 / ndf 2χ 108.3 / 110

Prob 0.5285

N 18728± 3.965e+05

m 0.0002± 0.4973

σ 0.000259± 0.007799

ν 0.519± 2.556

0

p 15.67± 32.82

1p 0.0713± 0.4789

2p 4.36± 42.34

3

p 12.38± -81.82

4p 10.13± 45.64


0.000215±mass = 0.497348

0.000259± = 0.007799σ 254±) in range = 3090

s

0 N(K

S/B = 3.766627

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 108.3 / 110

Prob 0.5285

N 18728± 3.965e+05

m 0.0002± 0.4973

σ 0.000259± 0.007799

ν 0.519± 2.556

0

p 15.67± 32.82

1p 0.0713± 0.4789

2p 4.36± 42.34

3

p 12.38± -81.82

4p 10.13± 45.64

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500 / ndf 2χ 108.3 / 110

Prob 0.5285

N 18728± 3.965e+05

m 0.0002± 0.4973

σ 0.000259± 0.007799

ν 0.519± 2.556

0

p 15.67± 32.82

1p 0.0713± 0.4789

2p 4.36± 42.34

3

p 12.38± -81.82

4p 10.13± 45.64


0.000215±mass = 0.497348

0.000259± = 0.007799σ 254±) in range = 3090

s

0 N(K

S/B = 3.766627

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500 / ndf 2χ 108.8 / 110

Prob 0.5132

N 20271± 4.236e+05

m 0.0002± 0.4973

σ 0.000275± 0.008732

ν 0.384± 2.094

0

p 3.67± 20.12

1p 0.1123± 0.3721

2p 4.0± 31.5

3

p 13.79± -45.64

4p 11.75± 16.96


0.000215±mass = 0.497255

0.000275± = 0.008732σ 302±) in range = 3691

s

0 N(K

S/B = 5.725384

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 108.8 / 110

Prob 0.5132

N 20271± 4.236e+05

m 0.0002± 0.4973

σ 0.000275± 0.008732

ν 0.384± 2.094

0

p 3.67± 20.12

1p 0.1123± 0.3721

2p 4.0± 31.5

3

p 13.79± -45.64

4p 11.75± 16.96

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500 / ndf 2χ 108.8 / 110

Prob 0.5132

N 20271± 4.236e+05

m 0.0002± 0.4973

σ 0.000275± 0.008732

ν 0.384± 2.094

0

p 3.67± 20.12

1p 0.1123± 0.3721

2p 4.0± 31.5

3

p 13.79± -45.64

4p 11.75± 16.96


0.000215±mass = 0.497255

0.000275± = 0.008732σ 302±) in range = 3691

s

0 N(K

S/B = 5.725384

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

400

450

/ ndf 2χ 99.35 / 110

Prob 0.7571

N 22148± 4.103e+05

m 0.0002± 0.4978 σ 0.00030± 0.01047 ν 0.278± 1.465

0p 5.92± 20.94

1

p 0.1811± 0.5193

2p 5.88± 32.04

3

p 19.27± -47.59

4p 15.75± 18.41


0.000246±mass = 0.497767

0.000301± = 0.010472σ 382±) in range = 4244

s

0 N(K

S/B = 8.282987

Range = [0.344000,0.700000]

Bin 5

/ ndf 2χ 99.35 / 110

Prob 0.7571

N 22148± 4.103e+05

m 0.0002± 0.4978 σ 0.00030± 0.01047 ν 0.278± 1.465

0p 5.92± 20.94

1

p 0.1811± 0.5193

2p 5.88± 32.04

3

p 19.27± -47.59

4p 15.75± 18.41

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

400

450

/ ndf 2χ 99.35 / 110

Prob 0.7571

N 22148± 4.103e+05

m 0.0002± 0.4978 σ 0.00030± 0.01047 ν 0.278± 1.465

0p 5.92± 20.94

1

p 0.1811± 0.5193

2p 5.88± 32.04

3

p 19.27± -47.59

4p 15.75± 18.41


0.000246±mass = 0.497767

0.000301± = 0.010472σ 382±) in range = 4244

s

0 N(K

S/B = 8.282987

Range = [0.344000,0.700000]

Bin 5

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV0

5

10

15

20

25

30

35

/ ndf 2χ 62.84 / 91

Prob 0.9893

N 1810± 1.875e+04

m 0.0011± 0.4974 σ 0.00106± 0.01427 ν 1829.4± 132.1

0p 0.8282± 0.2704

1

p 0.4492± 0.1196

2p 19.00± 41.37

3

p 47.8± -67.1

4p 36.3± 33.5

/ ndf 2χ 141.3 / 104

Prob 0.008742

N 24286± 2.632e+05

m 0.0003± 0.4972

σ 0.000376± 0.007123

ν 0.448± 1.394

0

p 14.92± 15.62

1p 0.1313± 0.1598

2p 6.83± 48.41

3

p 17.2± -101.5

4p 13.06± 63.47

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

/ ndf 2χ 141.3 / 104

Prob 0.008742

N 24286± 2.632e+05

m 0.0003± 0.4972

σ 0.000376± 0.007123

ν 0.448± 1.394

0

p 14.92± 15.62

1p 0.1313± 0.1598

2p 6.83± 48.41

3

p 17.2± -101.5

4p 13.06± 63.47


0.000284±mass = 0.497151

0.000376± = 0.007123σ 291±) in range = 1857

s

0 N(K

S/B = 1.790885

Range = [0.360000,0.700000]

Bin 1

/ ndf 2χ 128 / 109

Prob 0.103

N 15569± 4.173e+05

m 0.0002± 0.4969

σ 0.000220± 0.007777

ν 0.384± 3.485

0

p 0.0112± 0.0528

1p 0.0539± 0.2959

2p 2.54± 80.37

3

p 7.7± -156.7

4p 6.31± 94.35

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

100

200

300

400

500

/ ndf 2χ 128 / 109

Prob 0.103

N 15569± 4.173e+05

m 0.0002± 0.4969

σ 0.000220± 0.007777

ν 0.384± 3.485

0

p 0.0112± 0.0528

1p 0.0539± 0.2959

2p 2.54± 80.37

3

p 7.7± -156.7

4p 6.31± 94.35


0.000211±mass = 0.496889

0.000220± = 0.007777σ 216±) in range = 3245

s

0 N(K

S/B = 2.934986

Range = [0.345000,0.700000]

Bin 2

/ ndf 2χ 108.3 / 110

Prob 0.5285

N 18728± 3.965e+05

m 0.0002± 0.4973

σ 0.000259± 0.007799

ν 0.519± 2.556

0

p 15.67± 32.82

1p 0.0713± 0.4789

2p 4.36± 42.34

3

p 12.38± -81.82

4p 10.13± 45.64

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500 / ndf 2χ 108.3 / 110

Prob 0.5285

N 18728± 3.965e+05

m 0.0002± 0.4973

σ 0.000259± 0.007799

ν 0.519± 2.556

0

p 15.67± 32.82

1p 0.0713± 0.4789

2p 4.36± 42.34

3

p 12.38± -81.82

4p 10.13± 45.64


0.000215±mass = 0.497348

0.000259± = 0.007799σ 254±) in range = 3090

s

0 N(K

S/B = 3.766627

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 108.8 / 110

Prob 0.5132

N 20271± 4.236e+05

m 0.0002± 0.4973

σ 0.000275± 0.008732

ν 0.384± 2.094

0

p 3.67± 20.12

1p 0.1123± 0.3721

2p 4.0± 31.5

3

p 13.79± -45.64

4p 11.75± 16.96

-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500 / ndf 2χ 108.8 / 110

Prob 0.5132

N 20271± 4.236e+05

m 0.0002± 0.4973

σ 0.000275± 0.008732

ν 0.384± 2.094

0

p 3.67± 20.12

1p 0.1123± 0.3721

2p 4.0± 31.5

3

p 13.79± -45.64

4p 11.75± 16.96


0.000215±mass = 0.497255

0.000275± = 0.008732σ 302±) in range = 3691

s

0 N(K

S/B = 5.725384

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 99.35 / 110

Prob 0.7571

N 22148± 4.103e+05

m 0.0002± 0.4978

σ 0.00030± 0.01047

ν 0.278± 1.465

0p 5.92± 20.94

1

p 0.1811± 0.5193

2p 5.88± 32.04

3

p 19.27± -47.59

4p 15.75± 18.41

-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

400

450

/ ndf 2χ 99.35 / 110

Prob 0.7571

N 22148± 4.103e+05

m 0.0002± 0.4978

σ 0.00030± 0.01047

ν 0.278± 1.465

0p 5.92± 20.94

1

p 0.1811± 0.5193

2p 5.88± 32.04

3

p 19.27± -47.59

4p 15.75± 18.41


0.000246±mass = 0.497767

0.000301± = 0.010472σ 382±) in range = 4244

s

0 N(K

S/B = 8.282987

Range = [0.344000,0.700000]

Bin 5

/ ndf 2χ 62.84 / 91

Prob 0.9893

N 1810± 1.875e+04

m 0.0011± 0.4974

σ 0.00106± 0.01427

ν 1829.4± 132.1

0p 0.8282± 0.2704

1

p 0.4492± 0.1196

2p 19.00± 41.37

3

p 47.8± -67.1

4p 36.3± 33.5

-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV0

5

10

15

20

25

30

35

/ ndf 2χ 62.84 / 91

Prob 0.9893

N 1810± 1.875e+04

m 0.0011± 0.4974

σ 0.00106± 0.01427

ν 1829.4± 132.1

0p 0.8282± 0.2704

1

p 0.4492± 0.1196

2p 19.00± 41.37

3

p 47.8± -67.1

4p 36.3± 33.5

/ ndf 2χ 141.3 / 104

Prob 0.008742

N 24286± 2.632e+05

m 0.0003± 0.4972

σ 0.000376± 0.007123

ν 0.448± 1.394

0p 14.92± 15.62

1

p 0.1313± 0.1598

2p 6.83± 48.41

3

p 17.2± -101.5

4p 13.06± 63.47

-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

/ ndf 2χ 141.3 / 104

Prob 0.008742

N 24286± 2.632e+05

m 0.0003± 0.4972

σ 0.000376± 0.007123

ν 0.448± 1.394

0p 14.92± 15.62

1

p 0.1313± 0.1598

2p 6.83± 48.41

3

p 17.2± -101.5

4p 13.06± 63.47


0.000284±mass = 0.497151

0.000376± = 0.007123σ 291±) in range = 1857

s

0 N(K

S/B = 1.790885Range = [0.360000,0.700000]

Bin 1

/ ndf 2χ 128 / 109

Prob 0.103

N 15569± 4.173e+05

m 0.0002± 0.4969

σ 0.000220± 0.007777

ν 0.384± 3.485

0p 0.0112± 0.0528

1

p 0.0539± 0.2959

2p 2.54± 80.37

3

p 7.7± -156.7

4p 6.31± 94.35

-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV0

100

200

300

400

500

/ ndf 2χ 128 / 109

Prob 0.103

N 15569± 4.173e+05

m 0.0002± 0.4969

σ 0.000220± 0.007777

ν 0.384± 3.485

0p 0.0112± 0.0528

1

p 0.0539± 0.2959

2p 2.54± 80.37

3

p 7.7± -156.7

4p 6.31± 94.35


0.000211±mass = 0.496889

0.000220± = 0.007777σ 216±) in range = 3245

s

0 N(K

S/B = 2.934986Range = [0.345000,0.700000]

Bin 2

/ ndf 2χ 108.3 / 110

Prob 0.5285

N 18728± 3.965e+05

m 0.0002± 0.4973

σ 0.000259± 0.007799

ν 0.519± 2.556

0p 15.67± 32.82

1

p 0.0713± 0.4789

2p 4.36± 42.34

3

p 12.38± -81.82

4p 10.13± 45.64

-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500 / ndf 2χ 108.3 / 110

Prob 0.5285

N 18728± 3.965e+05

m 0.0002± 0.4973

σ 0.000259± 0.007799

ν 0.519± 2.556

0p 15.67± 32.82

1

p 0.0713± 0.4789

2p 4.36± 42.34

3

p 12.38± -81.82

4p 10.13± 45.64


0.000215±mass = 0.497348

0.000259± = 0.007799σ 254±) in range = 3090

s

0 N(K

S/B = 3.766627Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 108.8 / 110

Prob 0.5132

N 20271± 4.236e+05

m 0.0002± 0.4973

σ 0.000275± 0.008732

ν 0.384± 2.094

0p 3.67± 20.12

1

p 0.1123± 0.3721

2p 4.0± 31.5

3

p 13.79± -45.64

4p 11.75± 16.96

-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500 / ndf 2χ 108.8 / 110

Prob 0.5132

N 20271± 4.236e+05

m 0.0002± 0.4973

σ 0.000275± 0.008732

ν 0.384± 2.094

0p 3.67± 20.12

1

p 0.1123± 0.3721

2p 4.0± 31.5

3

p 13.79± -45.64

4p 11.75± 16.96


0.000215±mass = 0.497255

0.000275± = 0.008732σ 302±) in range = 3691

s

0 N(K

S/B = 5.725384Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 99.35 / 110

Prob 0.7571

N 22148± 4.103e+05

m 0.0002± 0.4978 σ 0.00030± 0.01047

ν 0.278± 1.465

0p 5.92± 20.94

1

p 0.1811± 0.5193

2p 5.88± 32.04

3

p 19.27± -47.59

4p 15.75± 18.41

-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

400

450

/ ndf 2χ 99.35 / 110

Prob 0.7571

N 22148± 4.103e+05

m 0.0002± 0.4978 σ 0.00030± 0.01047

ν 0.278± 1.465

0p 5.92± 20.94

1

p 0.1811± 0.5193

2p 5.88± 32.04

3

p 19.27± -47.59

4p 15.75± 18.41


0.000246±mass = 0.497767

0.000301± = 0.010472σ 382±) in range = 4244

s

0 N(K

S/B = 8.282987Range = [0.344000,0.700000]

Bin 5

/ ndf 2χ 62.84 / 91

Prob 0.9893

N 1810± 1.875e+04

m 0.0011± 0.4974 σ 0.00106± 0.01427

ν 1829.4± 132.1

0p 0.8282± 0.2704

1

p 0.4492± 0.1196

2p 19.00± 41.37

3

p 47.8± -67.1

4p 36.3± 33.5

-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV0

5

10

15

20

25

30

35

/ ndf 2χ 62.84 / 91

Prob 0.9893

N 1810± 1.875e+04

m 0.0011± 0.4974 σ 0.00106± 0.01427

ν 1829.4± 132.1

0p 0.8282± 0.2704

1

p 0.4492± 0.1196

2p

Figu

reF.6:

Fits

toth

ein

variant

mass

distrib

ution

fromdata

inbin

sof

xT

BF

pfor

the

targethem

isphere

inth

eB

reitFram

e.

156A

PP

EN

DIX

F.

FIT

ST

OM

ASS

DIS

TR

IBU

TIO

NS

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600 / ndf 2χ 130 / 109

Prob 0.08353

N 29890± 5.274e+05

m 0.0002± 0.4967

σ 0.000261± 0.008243

ν 0.325± 1.537

0

p 1.57± 28.22

1p 0.0591± 0.2837

2p 2.94± 48.89

3

p 10.4± -101.4

4p 9.1± 61.4


0.000207±mass = 0.496734

0.000261± = 0.008243σ 406±) in range = 4316

s

0 N(K

S/B = 2.850369

Range = [0.345000,0.700000]

Bin 1

/ ndf 2χ 130 / 109

Prob 0.08353

N 29890± 5.274e+05

m 0.0002± 0.4967

σ 0.000261± 0.008243

ν 0.325± 1.537

0

p 1.57± 28.22

1p 0.0591± 0.2837

2p 2.94± 48.89

3

p 10.4± -101.4

4p 9.1± 61.4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600 / ndf 2χ 130 / 109

Prob 0.08353

N 29890± 5.274e+05

m 0.0002± 0.4967

σ 0.000261± 0.008243

ν 0.325± 1.537

0

p 1.57± 28.22

1p 0.0591± 0.2837

2p 2.94± 48.89

3

p 10.4± -101.4

4p 9.1± 61.4


0.000207±mass = 0.496734

0.000261± = 0.008243σ 406±) in range = 4316

s

0 N(K

S/B = 2.850369

Range = [0.345000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 111.9 / 110

Prob 0.4319

N 32556± 6.148e+05

m 0.0002± 0.4965

σ 0.000254± 0.008728

ν 0.217± 1.273

0

p 2.1± 25.1

1p 0.0986± 0.4588

2p 4.10± 46.84

3

p 13.76± -97.46

4p 11.70± 60.54


0.000190±mass = 0.496463

0.000254± = 0.008728σ 477±) in range = 5284

s

0 N(K

S/B = 6.249479

Range = [0.344000,0.700000]

Bin 2

/ ndf 2χ 111.9 / 110

Prob 0.4319

N 32556± 6.148e+05

m 0.0002± 0.4965

σ 0.000254± 0.008728

ν 0.217± 1.273

0

p 2.1± 25.1

1p 0.0986± 0.4588

2p 4.10± 46.84

3

p 13.76± -97.46

4p 11.70± 60.54

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 111.9 / 110

Prob 0.4319

N 32556± 6.148e+05

m 0.0002± 0.4965

σ 0.000254± 0.008728

ν 0.217± 1.273

0

p 2.1± 25.1

1p 0.0986± 0.4588

2p 4.10± 46.84

3

p 13.76± -97.46

4p 11.70± 60.54


0.000190±mass = 0.496463

0.000254± = 0.008728σ 477±) in range = 5284

s

0 N(K

S/B = 6.249479

Range = [0.344000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 112.9 / 109

Prob 0.3808

N 17733± 6.874e+05

m 0.0002± 0.4967

σ 0.000265± 0.008968

ν 0.1± 1

0

p 3.81± 20.11

1p 0.2375± 0.6983

2p 7.66± 40.83

3

p 23.2± -72

4p 18.04± 36.61


0.000183±mass = 0.496700

0.000265± = 0.008968σ 358±) in range = 5962

s

0 N(K

S/B = 9.374162

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 112.9 / 109

Prob 0.3808

N 17733± 6.874e+05

m 0.0002± 0.4967

σ 0.000265± 0.008968

ν 0.1± 1

0

p 3.81± 20.11

1p 0.2375± 0.6983

2p 7.66± 40.83

3

p 23.2± -72

4p 18.04± 36.61

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 112.9 / 109

Prob 0.3808

N 17733± 6.874e+05

m 0.0002± 0.4967

σ 0.000265± 0.008968

ν 0.1± 1

0

p 3.81± 20.11

1p 0.2375± 0.6983

2p 7.66± 40.83

3

p 23.2± -72

4p 18.04± 36.61


0.000183±mass = 0.496700

0.000265± = 0.008968σ 358±) in range = 5962

s

0 N(K

S/B = 9.374162

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

400

450 / ndf 2χ 134.2 / 109

Prob 0.05073

N 22251± 4.147e+05

m 0.0003± 0.4966 σ 0.00037± 0.01118 ν 0.207± 1.221

0p 11.26± 25.36

1

p 0.460± 1.069

2p 13.05± 39.01

3

p 38.86± -63.75

4p 29.4± 27.6


0.000266±mass = 0.496632

0.000367± = 0.011184σ 442±) in range = 4529

s

0 N(K

S/B = 11.033285

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 134.2 / 109

Prob 0.05073

N 22251± 4.147e+05

m 0.0003± 0.4966 σ 0.00037± 0.01118 ν 0.207± 1.221

0p 11.26± 25.36

1

p 0.460± 1.069

2p 13.05± 39.01

3

p 38.86± -63.75

4p 29.4± 27.6

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

400

450 / ndf 2χ 134.2 / 109

Prob 0.05073

N 22251± 4.147e+05

m 0.0003± 0.4966 σ 0.00037± 0.01118 ν 0.207± 1.221

0p 11.26± 25.36

1

p 0.460± 1.069

2p 13.05± 39.01

3

p 38.86± -63.75

4p 29.4± 27.6


0.000266±mass = 0.496632

0.000367± = 0.011184σ 442±) in range = 4529

s

0 N(K

S/B = 11.033285

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

20

40

60

80

100

120

140

160

180

200 / ndf 2χ 114.3 / 106

Prob 0.2733

N 7518± 1.762e+05

m 0.0004± 0.4981 σ 0.00083± 0.01215 ν 0.1± 1

0p 8.14± 13.98

1

p 2.457± 3.435

2p 66.85± 89.31

3

p 180.7± -182.7

4p 128.2± 100.9


0.000424±mass = 0.498139

0.000830± = 0.012146σ 248±) in range = 2045

s

0 N(K

S/B = 7.613454

Range = [0.344000,0.700000]

Bin 5

Figu

reF.7:

Fits

toth

ein

variant

mass

distrib

ution

fromdata

inbin

sof

pC

BF

Tfor

the

curren

them

isphere

inth

eB

reitFram

e.

157

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

20

40

60

80

100

120

140

160

/ ndf 2χ 147 / 109

Prob 0.008888

N 21552± 1.417e+05

m 0.0004± 0.4967

σ 0.000533± 0.006248

ν 1.270± 1.047

0

p 3.12± 42.03

1p 0.0753± 0.3124

2p 3.4± 46.9

3

p 11.8± -106.1

4p 10.19± 70.31


0.000381±mass = 0.496703

0.000533± = 0.006248σ 238±) in range = 868

s

0 N(K

S/B = 1.153838

Range = [0.345000,0.700000]

Bin 1

/ ndf 2χ 147 / 109

Prob 0.008888

N 21552± 1.417e+05

m 0.0004± 0.4967

σ 0.000533± 0.006248

ν 1.270± 1.047

0

p 3.12± 42.03

1p 0.0753± 0.3124

2p 3.4± 46.9

3

p 11.8± -106.1

4p 10.19± 70.31

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

20

40

60

80

100

120

140

160

/ ndf 2χ 147 / 109

Prob 0.008888

N 21552± 1.417e+05

m 0.0004± 0.4967

σ 0.000533± 0.006248

ν 1.270± 1.047

0

p 3.12± 42.03

1p 0.0753± 0.3124

2p 3.4± 46.9

3

p 11.8± -106.1

4p 10.19± 70.31


0.000381±mass = 0.496703

0.000533± = 0.006248σ 238±) in range = 868

s

0 N(K

S/B = 1.153838

Range = [0.345000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

50

100

150

200

250

300

350

400 / ndf 2χ 108.3 / 104

Prob 0.3672

N 17654± 3.152e+05

m 0.0002± 0.4971

σ 0.000279± 0.007217

ν 0.790± 2.951

0

p 2.75± 25.26

1p 0.12134± 0.04328

2p 4.25± 39.26

3

p 13.50± -75.18

4p 10.94± 42.48


0.000233±mass = 0.497071

0.000279± = 0.007217σ 220±) in range = 2273

s

0 N(K

S/B = 2.092653

Range = [0.360000,0.700000]

Bin 2

/ ndf 2χ 108.3 / 104

Prob 0.3672

N 17654± 3.152e+05

m 0.0002± 0.4971

σ 0.000279± 0.007217

ν 0.790± 2.951

0

p 2.75± 25.26

1p 0.12134± 0.04328

2p 4.25± 39.26

3

p 13.50± -75.18

4p 10.94± 42.48

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

50

100

150

200

250

300

350

400 / ndf 2χ 108.3 / 104

Prob 0.3672

N 17654± 3.152e+05

m 0.0002± 0.4971

σ 0.000279± 0.007217

ν 0.790± 2.951

0

p 2.75± 25.26

1p 0.12134± 0.04328

2p 4.25± 39.26

3

p 13.50± -75.18

4p 10.94± 42.48


0.000233±mass = 0.497071

0.000279± = 0.007217σ 220±) in range = 2273

s

0 N(K

S/B = 2.092653

Range = [0.360000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

/ ndf 2χ 100.7 / 104

Prob 0.5743

N 18564± 5.178e+05

m 0.000± 0.497

σ 0.000207± 0.008223

ν 0.701± 3.732

0

p 1.98± 16.02

1p 0.1442± 0.1445

2p 4.74± 37.14

3

p 14.65± -61.88

4p 11.57± 30.02


0.000186±mass = 0.497023

0.000207± = 0.008223σ 264±) in range = 4257

s

0 N(K

S/B = 3.708699

Range = [0.360000,0.700000]

Bin 3

/ ndf 2χ 100.7 / 104

Prob 0.5743

N 18564± 5.178e+05

m 0.000± 0.497

σ 0.000207± 0.008223

ν 0.701± 3.732

0

p 1.98± 16.02

1p 0.1442± 0.1445

2p 4.74± 37.14

3

p 14.65± -61.88

4p 11.57± 30.02

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

/ ndf 2χ 100.7 / 104

Prob 0.5743

N 18564± 5.178e+05

m 0.000± 0.497

σ 0.000207± 0.008223

ν 0.701± 3.732

0

p 1.98± 16.02

1p 0.1442± 0.1445

2p 4.74± 37.14

3

p 14.65± -61.88

4p 11.57± 30.02


0.000186±mass = 0.497023

0.000207± = 0.008223σ 264±) in range = 4257

s

0 N(K

S/B = 3.708699

Range = [0.360000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 109.5 / 110

Prob 0.4961

N 23308± 5.937e+05

m 0.0002± 0.4974 σ 0.00023± 0.00864 ν 0.287± 2.081

0p 101.4± 172.6

1

p 0.0970± 0.4927

2p 5.4± 25.9

3

p 14.81± -42.41

4p 11.77± 18.23


0.000179±mass = 0.497419

0.000228± = 0.008640σ 346±) in range = 5118

s

0 N(K

S/B = 7.226262

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 109.5 / 110

Prob 0.4961

N 23308± 5.937e+05

m 0.0002± 0.4974 σ 0.00023± 0.00864 ν 0.287± 2.081

0p 101.4± 172.6

1

p 0.0970± 0.4927

2p 5.4± 25.9

3

p 14.81± -42.41

4p 11.77± 18.23

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 109.5 / 110

Prob 0.4961

N 23308± 5.937e+05

m 0.0002± 0.4974 σ 0.00023± 0.00864 ν 0.287± 2.081

0p 101.4± 172.6

1

p 0.0970± 0.4927

2p 5.4± 25.9

3

p 14.81± -42.41

4p 11.77± 18.23


0.000179±mass = 0.497419

0.000228± = 0.008640σ 346±) in range = 5118

s

0 N(K

S/B = 7.226262

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

400

450 / ndf 2χ 106.1 / 109

Prob 0.5615

N 23896± 3.648e+05

m 0.0003± 0.4979 σ 0.00042± 0.01222 ν 0.241± 1.163

0p 2.439± 4.536

1

p 0.3399± 0.4476

2p 9.69± 28.14

3

p 31.08± -29.66

4p 24.565± 4.239


0.000296±mass = 0.497945

0.000421± = 0.012221σ 500±) in range = 4324

s

0 N(K

S/B = 15.284040

Range = [0.344000,0.700000]

Bin 5

Figu

reF.8:

Fit

toth

ein

variant

mass

distrib

ution

fromdata

inbin

sof

pT

BF

Tfor

the

targethem

isphere

inth

eB

reitFram

e.

158A

PP

EN

DIX

F.

FIT

ST

OM

ASS

DIS

TR

IBU

TIO

NS

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 142.7 / 110

Prob 0.01973

N 6655± 6.523e+05

m 0.0000± 0.4982

σ 0.000047± 0.006554

ν 0.064± 1.907

0

p 2.25± 95.76

1p 0.0240± 0.3779

2p 1.09± 33.66

3

p 3.7± -67.7

4p 3.20± 38.51

Django MC/NDF ~ 1.2969002χ

0.000039±mass = 0.498236

0.000047± = 0.006554σ 75±) in range = 4267

s

0 N(K

S/B = 8.008803

Range = [0.344000,0.700000]

Bin 1

/ ndf 2χ 142.7 / 110

Prob 0.01973

N 6655± 6.523e+05

m 0.0000± 0.4982

σ 0.000047± 0.006554

ν 0.064± 1.907

0

p 2.25± 95.76

1p 0.0240± 0.3779

2p 1.09± 33.66

3

p 3.7± -67.7

4p 3.20± 38.51

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 142.7 / 110

Prob 0.01973

N 6655± 6.523e+05

m 0.0000± 0.4982

σ 0.000047± 0.006554

ν 0.064± 1.907

0

p 2.25± 95.76

1p 0.0240± 0.3779

2p 1.09± 33.66

3

p 3.7± -67.7

4p 3.20± 38.51


0.000039±mass = 0.498236

0.000047± = 0.006554σ 75±) in range = 4267

s

0 N(K

S/B = 8.008803

Range = [0.344000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200 / ndf 2χ 182.6 / 110

Prob 1.67e-05

N 8798± 1.042e+06

m 0.0000± 0.4982

σ 0.000040± 0.006661

ν 0.054± 1.911

0

p 16.1± 139

1p 0.0170± 0.3685

2p 1.11± 32.58

3

p 3.18± -62.36

4p 2.60± 33.43


0.000032±mass = 0.498155

0.000040± = 0.006661σ 101±) in range = 6929

s

0 N(K

S/B = 7.475634

Range = [0.344000,0.700000]

Bin 2

/ ndf 2χ 182.6 / 110

Prob 1.67e-05

N 8798± 1.042e+06

m 0.0000± 0.4982

σ 0.000040± 0.006661

ν 0.054± 1.911

0

p 16.1± 139

1p 0.0170± 0.3685

2p 1.11± 32.58

3

p 3.18± -62.36

4p 2.60± 33.43

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200 / ndf 2χ 182.6 / 110

Prob 1.67e-05

N 8798± 1.042e+06

m 0.0000± 0.4982

σ 0.000040± 0.006661

ν 0.054± 1.911

0

p 16.1± 139

1p 0.0170± 0.3685

2p 1.11± 32.58

3

p 3.18± -62.36

4p 2.60± 33.43


0.000032±mass = 0.498155

0.000040± = 0.006661σ 101±) in range = 6929

s

0 N(K

S/B = 7.475634

Range = [0.344000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

1600

/ ndf 2χ 182.7 / 110

Prob 1.659e-05

N 10359± 1.58e+06

m 0.0000± 0.4982

σ 0.000030± 0.006758

ν 0.037± 1.731

0

p 6.88± 52.15

1p 0.0135± 0.3751

2p 0.95± 42.79

3

p 2.52± -85.17

4p 2.02± 49.74


0.000025±mass = 0.498210

0.000030± = 0.006758σ 120±) in range = 10646

s

0 N(K

S/B = 7.292815

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 182.7 / 110

Prob 1.659e-05

N 10359± 1.58e+06

m 0.0000± 0.4982

σ 0.000030± 0.006758

ν 0.037± 1.731

0

p 6.88± 52.15

1p 0.0135± 0.3751

2p 0.95± 42.79

3

p 2.52± -85.17

4p 2.02± 49.74

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

1600

/ ndf 2χ 182.7 / 110

Prob 1.659e-05

N 10359± 1.58e+06

m 0.0000± 0.4982

σ 0.000030± 0.006758

ν 0.037± 1.731

0

p 6.88± 52.15

1p 0.0135± 0.3751

2p 0.95± 42.79

3

p 2.52± -85.17

4p 2.02± 49.74


0.000025±mass = 0.498210

0.000030± = 0.006758σ 120±) in range = 10646

s

0 N(K

S/B = 7.292815

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

1600

/ ndf 2χ 167.2 / 109

Prob 0.0002852

N 9620± 1.532e+06

m 0.0000± 0.4982

σ 0.000029± 0.007003

ν 0.034± 1.612

0

p 36.8± 217

1p 0.0151± 0.3307

2p 1.11± 32.06

3

p 2.67± -60.56

4p 2.04± 32.43


0.000023±mass = 0.498189

0.000029± = 0.007003σ 114±) in range = 10680

s

0 N(K

S/B = 6.391179

Range = [0.345000,0.700000]

Bin 4

/ ndf 2χ 167.2 / 109

Prob 0.0002852

N 9620± 1.532e+06

m 0.0000± 0.4982

σ 0.000029± 0.007003

ν 0.034± 1.612

0

p 36.8± 217

1p 0.0151± 0.3307

2p 1.11± 32.06

3

p 2.67± -60.56

4p 2.04± 32.43

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

1600

/ ndf 2χ 167.2 / 109

Prob 0.0002852

N 9620± 1.532e+06

m 0.0000± 0.4982

σ 0.000029± 0.007003

ν 0.034± 1.612

0

p 36.8± 217

1p 0.0151± 0.3307

2p 1.11± 32.06

3

p 2.67± -60.56

4p 2.04± 32.43


0.000023±mass = 0.498189

0.000029± = 0.007003σ 114±) in range = 10680

s

0 N(K

S/B = 6.391179

Range = [0.345000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800 / ndf 2χ 181.6 / 110

Prob 2.086e-05

N 6466± 7.128e+05

m 0.0000± 0.4982

σ 0.000042± 0.007379

ν 0.042± 1.546

0

p 0.357± 3.303

1p 0.015± 0.345

2p 1.01± 53.49

3

p 2.8± -100.3

4p 2.30± 56.44


0.000033±mass = 0.498178

0.000042± = 0.007379σ 80±) in range = 5229

s

0 N(K

S/B = 4.822199

Range = [0.344000,0.700000]

Bin 5

/ ndf 2χ 181.6 / 110

Prob 2.086e-05

N 6466± 7.128e+05

m 0.0000± 0.4982

σ 0.000042± 0.007379

ν 0.042± 1.546

0

p 0.357± 3.303

1p 0.015± 0.345

2p 1.01± 53.49

3

p 2.8± -100.3

4p 2.30± 56.44

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800 / ndf 2χ 181.6 / 110

Prob 2.086e-05

N 6466± 7.128e+05

m 0.0000± 0.4982

σ 0.000042± 0.007379

ν 0.042± 1.546

0

p 0.357± 3.303

1p 0.015± 0.345

2p 1.01± 53.49

3

p 2.8± -100.3

4p 2.30± 56.44


0.000033±mass = 0.498178

0.000042± = 0.007379σ 80±) in range = 5229

s

0 N(K

S/B = 4.822199

Range = [0.344000,0.700000]

Bin 5

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

/ ndf 2χ 140.3 / 110

Prob 0.02727

N 4358± 2.898e+05

m 0.0001± 0.4983

σ 0.000073± 0.008215

ν 0.067± 1.313

0

p 34.3± 155.5

1p 0.0152± 0.3398

2p 1.48± 30.58

3

p 3.43± -61.36

4p 2.59± 35.66


0.000057±mass = 0.498282

0.000073± = 0.008215σ 61±) in range = 2350

s

0 N(K

S/B = 3.313297

Range = [0.344000,0.700000]

Bin 6

Figu

reF.9:

Fits

toth

ein

variant

mass

distrib

ution

fromD

jango

Mon

teC

arloin

bin

sof

Q2.

159

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900

/ ndf 2χ 182.5 / 110

Prob 1.71e-05

N 6828± 8.571e+05

m 0.0000± 0.4983

σ 0.000037± 0.006616

ν 0.055± 2.027

0

p 37.5± 121.9

1p 0.0178± 0.3711

2p 1.92± 33.42

3

p 4.23± -66.19

4p 3.09± 36.86


0.000031±mass = 0.498311

0.000037± = 0.006616σ 78±) in range = 5662

s

0 N(K

S/B = 7.802170

Range = [0.344000,0.700000]

Bin 1

/ ndf 2χ 182.5 / 110

Prob 1.71e-05

N 6828± 8.571e+05

m 0.0000± 0.4983

σ 0.000037± 0.006616

ν 0.055± 2.027

0

p 37.5± 121.9

1p 0.0178± 0.3711

2p 1.92± 33.42

3

p 4.23± -66.19

4p 3.09± 36.86

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900

/ ndf 2χ 182.5 / 110

Prob 1.71e-05

N 6828± 8.571e+05

m 0.0000± 0.4983

σ 0.000037± 0.006616

ν 0.055± 2.027

0

p 37.5± 121.9

1p 0.0178± 0.3711

2p 1.92± 33.42

3

p 4.23± -66.19

4p 3.09± 36.86


0.000031±mass = 0.498311

0.000037± = 0.006616σ 78±) in range = 5662

s

0 N(K

S/B = 7.802170

Range = [0.344000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

500

1000

1500

2000

2500

/ ndf 2χ 216.7 / 109

Prob 4.026e-09

N 12558± 2.393e+06

m 0.0000± 0.4982

σ 0.000024± 0.006658

ν 0.031± 1.775

0

p 7.54± 45.55

1p 0.0144± 0.3265

2p 1.11± 43.32

3

p 2.62± -83.16

4p 1.96± 47.06


0.000020±mass = 0.498170

0.000024± = 0.006658σ 143±) in range = 15888

s

0 N(K

S/B = 7.431128

Range = [0.345000,0.700000]

Bin 2

/ ndf 2χ 216.7 / 109

Prob 4.026e-09

N 12558± 2.393e+06

m 0.0000± 0.4982

σ 0.000024± 0.006658

ν 0.031± 1.775

0

p 7.54± 45.55

1p 0.0144± 0.3265

2p 1.11± 43.32

3

p 2.62± -83.16

4p 1.96± 47.06

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

500

1000

1500

2000

2500

/ ndf 2χ 216.7 / 109

Prob 4.026e-09

N 12558± 2.393e+06

m 0.0000± 0.4982

σ 0.000024± 0.006658

ν 0.031± 1.775

0

p 7.54± 45.55

1p 0.0144± 0.3265

2p 1.11± 43.32

3

p 2.62± -83.16

4p 1.96± 47.06


0.000020±mass = 0.498170

0.000024± = 0.006658σ 143±) in range = 15888

s

0 N(K

S/B = 7.431128

Range = [0.345000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

1600

1800

2000 / ndf 2χ 184.3 / 109

Prob 8.905e-06

N 11613± 1.816e+06

m 0.0000± 0.4982

σ 0.00003± 0.00705 ν 0.03± 1.54

0p 355.3± 1539

1

p 0.0154± 0.3763

2p 1.32± 23.42

3

p 2.92± -45.92

4p 2.14± 24.05


0.000023±mass = 0.498176

0.000029± = 0.007050σ 139±) in range = 12733

s

0 N(K

S/B = 6.422628

Range = [0.345000,0.700000]

Bin 3

/ ndf 2χ 184.3 / 109

Prob 8.905e-06

N 11613± 1.816e+06

m 0.0000± 0.4982

σ 0.00003± 0.00705 ν 0.03± 1.54

0p 355.3± 1539

1

p 0.0154± 0.3763

2p 1.32± 23.42

3

p 2.92± -45.92

4p 2.14± 24.05

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

1600

1800

2000 / ndf 2χ 184.3 / 109

Prob 8.905e-06

N 11613± 1.816e+06

m 0.0000± 0.4982

σ 0.00003± 0.00705 ν 0.03± 1.54

0p 355.3± 1539

1

p 0.0154± 0.3763

2p 1.32± 23.42

3

p 2.92± -45.92

4p 2.14± 24.05


0.000023±mass = 0.498176

0.000029± = 0.007050σ 139±) in range = 12733

s

0 N(K

S/B = 6.422628

Range = [0.345000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

/ ndf 2χ 193.7 / 110

Prob 1.479e-06

N 7019± 7.642e+05

m 0.0000± 0.4982

σ 0.000043± 0.007904

ν 0.046± 1.447

0

p 20.8± 149.3

1p 0.011± 0.347

2p 0.96± 34.83

3

p 2.33± -67.94

4p 1.80± 38.53


0.000032±mass = 0.498190

0.000043± = 0.007904σ 93±) in range = 5989

s

0 N(K

S/B = 3.895350

Range = [0.344000,0.700000]

Bin 4

Figu

reF.10:

Fits

toth

ein

variant

mass

distrib

ution

fromD

jango

Mon

teC

arloin

bin

sof

x.

160A

PP

EN

DIX

F.

FIT

ST

OM

ASS

DIS

TR

IBU

TIO

NS

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 218 / 110

Prob 4.051e-09

N 6621± 1.008e+06

m 0.0000± 0.4983

σ 0.000032± 0.006652

ν 0.051± 2.269

0

p 28.25± 50.18

1p 0.0196± 0.3306

2p 3.1± 36.2

3

p 6.13± -68.29

4p 4.05± 36.58


0.000027±mass = 0.498289

0.000032± = 0.006652σ 77±) in range = 6697

s

0 N(K

S/B = 9.132876

Range = [0.344000,0.700000]

Bin 1

/ ndf 2χ 218 / 110

Prob 4.051e-09

N 6621± 1.008e+06

m 0.0000± 0.4983

σ 0.000032± 0.006652

ν 0.051± 2.269

0

p 28.25± 50.18

1p 0.0196± 0.3306

2p 3.1± 36.2

3

p 6.13± -68.29

4p 4.05± 36.58

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 218 / 110

Prob 4.051e-09

N 6621± 1.008e+06

m 0.0000± 0.4983

σ 0.000032± 0.006652

ν 0.051± 2.269

0

p 28.25± 50.18

1p 0.0196± 0.3306

2p 3.1± 36.2

3

p 6.13± -68.29

4p 4.05± 36.58


0.000027±mass = 0.498289

0.000032± = 0.006652σ 77±) in range = 6697

s

0 N(K

S/B = 9.132876

Range = [0.344000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400 / ndf 2χ 213.3 / 110

Prob 1.358e-08

N 10406± 1.323e+06

m 0.0000± 0.4981

σ 0.00003± 0.00645 ν 0.031± 1.326

0p 21.97± 75.07

1

p 0.0185± 0.4221

2p 1.77± 37.55

3

p 3.93± -72.41

4p 2.89± 39.95


0.000026±mass = 0.498072

0.000033± = 0.006450σ 116±) in range = 8455

s

0 N(K

S/B = 8.349084

Range = [0.344000,0.700000]

Bin 2

/ ndf 2χ 213.3 / 110

Prob 1.358e-08

N 10406± 1.323e+06

m 0.0000± 0.4981

σ 0.00003± 0.00645 ν 0.031± 1.326

0p 21.97± 75.07

1

p 0.0185± 0.4221

2p 1.77± 37.55

3

p 3.93± -72.41

4p 2.89± 39.95

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400 / ndf 2χ 213.3 / 110

Prob 1.358e-08

N 10406± 1.323e+06

m 0.0000± 0.4981

σ 0.00003± 0.00645 ν 0.031± 1.326

0p 21.97± 75.07

1

p 0.0185± 0.4221

2p 1.77± 37.55

3

p 3.93± -72.41

4p 2.89± 39.95


0.000026±mass = 0.498072

0.000033± = 0.006450σ 116±) in range = 8455

s

0 N(K

S/B = 8.349084

Range = [0.344000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400 / ndf 2χ 221 / 110

Prob 1.888e-09

N 11064± 1.342e+06

m 0.0000± 0.4982

σ 0.000034± 0.006822

ν 0.030± 1.224

0

p 1.19± 64.87

1p 0.0163± 0.4188

2p 0.72± 40.03

3

p 2.52± -78.26

4p 2.20± 44.27


0.000027±mass = 0.498234

0.000034± = 0.006822σ 128±) in range = 9041

s

0 N(K

S/B = 7.401748

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 221 / 110

Prob 1.888e-09

N 11064± 1.342e+06

m 0.0000± 0.4982

σ 0.000034± 0.006822

ν 0.030± 1.224

0

p 1.19± 64.87

1p 0.0163± 0.4188

2p 0.72± 40.03

3

p 2.52± -78.26

4p 2.20± 44.27

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400 / ndf 2χ 221 / 110

Prob 1.888e-09

N 11064± 1.342e+06

m 0.0000± 0.4982

σ 0.000034± 0.006822

ν 0.030± 1.224

0

p 1.19± 64.87

1p 0.0163± 0.4188

2p 0.72± 40.03

3

p 2.52± -78.26

4p 2.20± 44.27


0.000027±mass = 0.498234

0.000034± = 0.006822σ 128±) in range = 9041

s

0 N(K

S/B = 7.401748

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

/ ndf 2χ 143.1 / 110

Prob 0.01854

N 8943± 1.328e+06

m 0.0000± 0.4982

σ 0.000031± 0.006756

ν 0.04± 1.85

0

p 26.1± 164.5

1p 0.0118± 0.3379

2p 0.98± 34.96

3

p 2.29± -68.97

4p 1.76± 39.38


0.000026±mass = 0.498201

0.000031± = 0.006756σ 103±) in range = 8954

s

0 N(K

S/B = 5.788455

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 143.1 / 110

Prob 0.01854

N 8943± 1.328e+06

m 0.0000± 0.4982

σ 0.000031± 0.006756

ν 0.04± 1.85

0

p 26.1± 164.5

1p 0.0118± 0.3379

2p 0.98± 34.96

3

p 2.29± -68.97

4p 1.76± 39.38

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400

/ ndf 2χ 143.1 / 110

Prob 0.01854

N 8943± 1.328e+06

m 0.0000± 0.4982

σ 0.000031± 0.006756

ν 0.04± 1.85

0

p 26.1± 164.5

1p 0.0118± 0.3379

2p 0.98± 34.96

3

p 2.29± -68.97

4p 1.76± 39.38


0.000026±mass = 0.498201

0.000031± = 0.006756σ 103±) in range = 8954

s

0 N(K

S/B = 5.788455

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000 / ndf 2χ 184.9 / 109

Prob 7.767e-06

N 7054± 8.634e+05

m 0.0000± 0.4982

σ 0.000045± 0.008263

ν 0.082± 2.389

0

p 12.09± 86.54

1p 0.0140± 0.3018

2p 1.02± 38.29

3

p 2.52± -73.36

4p 1.92± 41.21


0.000037±mass = 0.498205

0.000045± = 0.008263σ 98±) in range = 7126

s

0 N(K

S/B = 3.720535

Range = [0.345000,0.700000]

Bin 5

Figu

reF.11:

Fits

toth

ein

variant

mass

distrib

ution

fromD

jango

Mon

teC

arloin

bin

sof

η.

161

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400 / ndf 2χ 146.4 / 104

Prob 0.003892

N 8095± 1.145e+06

m 0.0000± 0.4984

σ 0.00003± 0.00579 ν 0.106± 3.189

0p 5.97± 30.46

1

p 0.0183± 0.2022

2p 1.21± 49.34

3

p 2.75± -98.74

4p 1.99± 57.72


0.000025±mass = 0.498387

0.000030± = 0.005790σ 81±) in range = 6629

s

0 N(K

S/B = 2.367369

Range = [0.360000,0.700000]

Bin 1

/ ndf 2χ 146.4 / 104

Prob 0.003892

N 8095± 1.145e+06

m 0.0000± 0.4984

σ 0.00003± 0.00579 ν 0.106± 3.189

0p 5.97± 30.46

1

p 0.0183± 0.2022

2p 1.21± 49.34

3

p 2.75± -98.74

4p 1.99± 57.72

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

1400 / ndf 2χ 146.4 / 104

Prob 0.003892

N 8095± 1.145e+06

m 0.0000± 0.4984

σ 0.00003± 0.00579 ν 0.106± 3.189

0p 5.97± 30.46

1

p 0.0183± 0.2022

2p 1.21± 49.34

3

p 2.75± -98.74

4p 1.99± 57.72


0.000025±mass = 0.498387

0.000030± = 0.005790σ 81±) in range = 6629

s

0 N(K

S/B = 2.367369

Range = [0.360000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

200

400

600

800

1000

/ ndf 2χ 145.9 / 110

Prob 0.0124

N 6929± 9.881e+05

m 0.0000± 0.4982

σ 0.000033± 0.006287

ν 0.075± 2.749

0

p 7.44± 49.68

1p 0.0159± 0.3829

2p 1.10± 39.22

3

p 2.82± -75.85

4p 2.20± 43.06


0.000028±mass = 0.498248

0.000033± = 0.006287σ 76±) in range = 6210

s

0 N(K

S/B = 6.199042

Range = [0.344000,0.700000]

Bin 2

/ ndf 2χ 145.9 / 110

Prob 0.0124

N 6929± 9.881e+05

m 0.0000± 0.4982

σ 0.000033± 0.006287

ν 0.075± 2.749

0

p 7.44± 49.68

1p 0.0159± 0.3829

2p 1.10± 39.22

3

p 2.82± -75.85

4p 2.20± 43.06

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

200

400

600

800

1000

/ ndf 2χ 145.9 / 110

Prob 0.0124

N 6929± 9.881e+05

m 0.0000± 0.4982

σ 0.000033± 0.006287

ν 0.075± 2.749

0

p 7.44± 49.68

1p 0.0159± 0.3829

2p 1.10± 39.22

3

p 2.82± -75.85

4p 2.20± 43.06


0.000028±mass = 0.498248

0.000033± = 0.006287σ 76±) in range = 6210

s

0 N(K

S/B = 6.199042

Range = [0.344000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

/ ndf 2χ 189.9 / 110

Prob 3.422e-06

N 7539± 1.163e+06

m 0.0000± 0.4981

σ 0.000032± 0.006786

ν 0.048± 2.157

0

p 16.59± 63.93

1p 0.0211± 0.4232

2p 1.66± 34.41

3

p 3.76± -63.74

4p 2.75± 34.65


0.000026±mass = 0.498129

0.000032± = 0.006786σ 89±) in range = 7881

s

0 N(K

S/B = 10.025541

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 189.9 / 110

Prob 3.422e-06

N 7539± 1.163e+06

m 0.0000± 0.4981

σ 0.000032± 0.006786

ν 0.048± 2.157

0

p 16.59± 63.93

1p 0.0211± 0.4232

2p 1.66± 34.41

3

p 3.76± -63.74

4p 2.75± 34.65

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

1200

/ ndf 2χ 189.9 / 110

Prob 3.422e-06

N 7539± 1.163e+06

m 0.0000± 0.4981

σ 0.000032± 0.006786

ν 0.048± 2.157

0

p 16.59± 63.93

1p 0.0211± 0.4232

2p 1.66± 34.41

3

p 3.76± -63.74

4p 2.75± 34.65


0.000026±mass = 0.498129

0.000032± = 0.006786σ 89±) in range = 7881

s

0 N(K

S/B = 10.025541

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 147.7 / 110

Prob 0.009555

N 7819± 1.077e+06

m 0.0000± 0.4981

σ 0.000037± 0.007435

ν 0.035± 1.608

0

p 2.19± 43.59

1p 0.0333± 0.4912

2p 1.10± 33.03

3

p 3.63± -58.85

4p 2.99± 31.37


0.000030±mass = 0.498054

0.000037± = 0.007435σ 100±) in range = 7968

s

0 N(K

S/B = 14.698323

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 147.7 / 110

Prob 0.009555

N 7819± 1.077e+06

m 0.0000± 0.4981

σ 0.000037± 0.007435

ν 0.035± 1.608

0

p 2.19± 43.59

1p 0.0333± 0.4912

2p 1.10± 33.03

3

p 3.63± -58.85

4p 2.99± 31.37

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 147.7 / 110

Prob 0.009555

N 7819± 1.077e+06

m 0.0000± 0.4981

σ 0.000037± 0.007435

ν 0.035± 1.608

0

p 2.19± 43.59

1p 0.0333± 0.4912

2p 1.10± 33.03

3

p 3.63± -58.85

4p 2.99± 31.37


0.000030±mass = 0.498054

0.000037± = 0.007435σ 100±) in range = 7968

s

0 N(K

S/B = 14.698323

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 182.5 / 110

Prob 1.711e-05

N 8022± 8.769e+05

m 0.0000± 0.4981

σ 0.000049± 0.008539

ν 0.027± 1.083

0

p 0.504± 8.398

1p 0.0830± 0.8357

2p 2.61± 46.45

3

p 7.71± -87.78

4p 5.85± 50.48


0.000037±mass = 0.498110

0.000049± = 0.008539σ 121±) in range = 7303

s

0 N(K

S/B = 19.699603

Range = [0.344000,0.700000]

Bin 5

/ ndf 2χ 182.5 / 110

Prob 1.711e-05

N 8022± 8.769e+05

m 0.0000± 0.4981

σ 0.000049± 0.008539

ν 0.027± 1.083

0

p 0.504± 8.398

1p 0.0830± 0.8357

2p 2.61± 46.45

3

p 7.71± -87.78

4p 5.85± 50.48

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 182.5 / 110

Prob 1.711e-05

N 8022± 8.769e+05

m 0.0000± 0.4981

σ 0.000049± 0.008539

ν 0.027± 1.083

0

p 0.504± 8.398

1p 0.0830± 0.8357

2p 2.61± 46.45

3

p 7.71± -87.78

4p 5.85± 50.48


0.000037±mass = 0.498110

0.000049± = 0.008539σ 121±) in range = 7303

s

0 N(K

S/B = 19.699603

Range = [0.344000,0.700000]

Bin 5

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV0

100

200

300

400

500 / ndf 2χ 334.5 / 109

Prob 9.477e-25

N 3330± 4.824e+05

m 0.0001± 0.4984 σ 0.00009± 0.01038 ν 0.0± 1

0p 8.53± 31.07

1

p 0.098± 1.287

2p 3.36± 49.24

3

p 9.0± -91.6

4p 6.62± 47.28


0.000058±mass = 0.498385

0.000091± = 0.010382σ 75±) in range = 4818

s

0 N(K

S/B = 7.711979

Range = [0.345000,0.700000]

Bin 6

Figu

reF.12:

Fits

toth

ein

variant

mass

distrib

ution

fromD

jango

Mon

teC

arloin

bin

sof

pT.

162A

PP

EN

DIX

F.

FIT

ST

OM

ASS

DIS

TR

IBU

TIO

NS

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

/ ndf 2χ 141.9 / 109

Prob 0.01869

N 6378± 6.947e+05

m 0.0000± 0.4982

σ 0.000040± 0.006214

ν 0.086± 2.351

0

p 10.11± 81.94

1p 0.0125± 0.3045

2p 0.90± 42.37

3

p 2.31± -87.32

4p 1.81± 51.91


0.000033±mass = 0.498178

0.000040± = 0.006214σ 68±) in range = 4314

s

0 N(K

S/B = 2.684429

Range = [0.345000,0.700000]

Bin 1

/ ndf 2χ 141.9 / 109

Prob 0.01869

N 6378± 6.947e+05

m 0.0000± 0.4982

σ 0.000040± 0.006214

ν 0.086± 2.351

0

p 10.11± 81.94

1p 0.0125± 0.3045

2p 0.90± 42.37

3

p 2.31± -87.32

4p 1.81± 51.91

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

/ ndf 2χ 141.9 / 109

Prob 0.01869

N 6378± 6.947e+05

m 0.0000± 0.4982

σ 0.000040± 0.006214

ν 0.086± 2.351

0

p 10.11± 81.94

1p 0.0125± 0.3045

2p 0.90± 42.37

3

p 2.31± -87.32

4p 1.81± 51.91


0.000033±mass = 0.498178

0.000040± = 0.006214σ 68±) in range = 4314

s

0 N(K

S/B = 2.684429

Range = [0.345000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 152.8 / 110

Prob 0.004359

N 7599± 9.539e+05

m 0.0000± 0.4981

σ 0.0000± 0.0068 ν 0.041± 1.628

0p 0.44± 17.22

1

p 0.0237± 0.4041

2p 0.92± 41.63

3

p 3.07± -78.03

4p 2.59± 43.52


0.000031±mass = 0.498090

0.000037± = 0.006800σ 89±) in range = 6459

s

0 N(K

S/B = 9.213581

Range = [0.344000,0.700000]

Bin 2

/ ndf 2χ 152.8 / 110

Prob 0.004359

N 7599± 9.539e+05

m 0.0000± 0.4981

σ 0.0000± 0.0068 ν 0.041± 1.628

0p 0.44± 17.22

1

p 0.0237± 0.4041

2p 0.92± 41.63

3

p 3.07± -78.03

4p 2.59± 43.52

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

200

400

600

800

1000

/ ndf 2χ 152.8 / 110

Prob 0.004359

N 7599± 9.539e+05

m 0.0000± 0.4981

σ 0.0000± 0.0068 ν 0.041± 1.628

0p 0.44± 17.22

1

p 0.0237± 0.4041

2p 0.92± 41.63

3

p 3.07± -78.03

4p 2.59± 43.52


0.000031±mass = 0.498090

0.000037± = 0.006800σ 89±) in range = 6459

s

0 N(K

S/B = 9.213581

Range = [0.344000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 151 / 110

Prob 0.00583

N 7348± 7.096e+05

m 0.0000± 0.4982

σ 0.000048± 0.007414

ν 0.034± 1.186

0

p 5.68± 10.65

1p 0.0658± 0.6843

2p 4.04± 42.84

3

p 9.53± -81.06

4p 6.84± 45.83


0.000038±mass = 0.498157

0.000048± = 0.007414σ 94±) in range = 5178

s

0 N(K

S/B = 17.177114

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 151 / 110

Prob 0.00583

N 7348± 7.096e+05

m 0.0000± 0.4982

σ 0.000048± 0.007414

ν 0.034± 1.186

0

p 5.68± 10.65

1p 0.0658± 0.6843

2p 4.04± 42.84

3

p 9.53± -81.06

4p 6.84± 45.83

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 151 / 110

Prob 0.00583

N 7348± 7.096e+05

m 0.0000± 0.4982

σ 0.000048± 0.007414

ν 0.034± 1.186

0

p 5.68± 10.65

1p 0.0658± 0.6843

2p 4.04± 42.84

3

p 9.53± -81.06

4p 6.84± 45.83


0.000038±mass = 0.498157

0.000048± = 0.007414σ 94±) in range = 5178

s

0 N(K

S/B = 17.177114

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

/ ndf 2χ 219.4 / 110

Prob 2.813e-09

N 6168± 5.117e+05

m 0.0000± 0.4981

σ 0.000064± 0.008063

ν 0.034± 1.056

0

p 8.43± 24.67

1p 0.148± 1.455

2p 4.36± 52.66

3

p 12.3± -105.1

4p 9.23± 58.83


0.000048±mass = 0.498101

0.000064± = 0.008063σ 89±) in range = 4022

s

0 N(K

S/B = 14.128829

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 219.4 / 110

Prob 2.813e-09

N 6168± 5.117e+05

m 0.0000± 0.4981

σ 0.000064± 0.008063

ν 0.034± 1.056

0

p 8.43± 24.67

1p 0.148± 1.455

2p 4.36± 52.66

3

p 12.3± -105.1

4p 9.23± 58.83

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

/ ndf 2χ 219.4 / 110

Prob 2.813e-09

N 6168± 5.117e+05

m 0.0000± 0.4981

σ 0.000064± 0.008063

ν 0.034± 1.056

0

p 8.43± 24.67

1p 0.148± 1.455

2p 4.36± 52.66

3

p 12.3± -105.1

4p 9.23± 58.83


0.000048±mass = 0.498101

0.000064± = 0.008063σ 89±) in range = 4022

s

0 N(K

S/B = 14.128829

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

20

40

60

80

100

120

140

160

180

200

/ ndf 2χ 160.8 / 110

Prob 0.001145

N 3995± 2.102e+05

m 0.0001± 0.4983

σ 0.000112± 0.008924

ν 0.052± 1.013

0

p 7.99± 14.58

1p 0.27± 1.57

2p 9.13± 46.34

3

p 23.54± -80.16

4p 16.79± 35.75


0.000080±mass = 0.498294

0.000112± = 0.008924σ 65±) in range = 1816

s

0 N(K

S/B = 11.103964

Range = [0.344000,0.700000]

Bin 5

Figu

reF.13:

Fits

toth

ein

variant

mass

distrib

ution

fromD

jango

Mon

teC

arloin

bin

sof

xC

BF

pfor

the

curren

them

isphere

inth

eB

reitFram

e.

163

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

/ ndf 2χ 95.03 / 101

Prob 0.6485

N 4268± 3.102e+05

m 0.0001± 0.4983

σ 0.000061± 0.006066

ν 0.204± 3.094

0

p 0.56± 16.65

1p 0.0451± 0.2212

2p 1.5± 45.5

3

p 4.43± -90.33

4p 3.48± 52.41


0.000050±mass = 0.498338

0.000061± = 0.006066σ 44±) in range = 1881

s

0 N(K

S/B = 2.071586

Range = [0.370000,0.700000]

Bin 1

/ ndf 2χ 95.03 / 101

Prob 0.6485

N 4268± 3.102e+05

m 0.0001± 0.4983

σ 0.000061± 0.006066

ν 0.204± 3.094

0

p 0.56± 16.65

1p 0.0451± 0.2212

2p 1.5± 45.5

3

p 4.43± -90.33

4p 3.48± 52.41

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250

300

350

/ ndf 2χ 95.03 / 101

Prob 0.6485

N 4268± 3.102e+05

m 0.0001± 0.4983

σ 0.000061± 0.006066

ν 0.204± 3.094

0

p 0.56± 16.65

1p 0.0451± 0.2212

2p 1.5± 45.5

3

p 4.43± -90.33

4p 3.48± 52.41


0.000050±mass = 0.498338

0.000061± = 0.006066σ 44±) in range = 1881

s

0 N(K

S/B = 2.071586

Range = [0.370000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

100

200

300

400

500

600

700 / ndf 2χ 121.6 / 110

Prob 0.211

N 5900± 6.158e+05

m 0.0000± 0.4983

σ 0.000043± 0.006168

ν 0.090± 2.466

0

p 14.98± 84.58

1p 0.0165± 0.3513

2p 1.3± 38

3

p 3.3± -78.6

4p 2.57± 46.77


0.000036±mass = 0.498317

0.000043± = 0.006168σ 63±) in range = 3796

s

0 N(K

S/B = 4.780039

Range = [0.344000,0.700000]

Bin 2

/ ndf 2χ 121.6 / 110

Prob 0.211

N 5900± 6.158e+05

m 0.0000± 0.4983

σ 0.000043± 0.006168

ν 0.090± 2.466

0

p 14.98± 84.58

1p 0.0165± 0.3513

2p 1.3± 38

3

p 3.3± -78.6

4p 2.57± 46.77

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

100

200

300

400

500

600

700 / ndf 2χ 121.6 / 110

Prob 0.211

N 5900± 6.158e+05

m 0.0000± 0.4983

σ 0.000043± 0.006168

ν 0.090± 2.466

0

p 14.98± 84.58

1p 0.0165± 0.3513

2p 1.3± 38

3

p 3.3± -78.6

4p 2.57± 46.77


0.000036±mass = 0.498317

0.000043± = 0.006168σ 63±) in range = 3796

s

0 N(K

S/B = 4.780039

Range = [0.344000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

/ ndf 2χ 173.7 / 110

Prob 0.0001027

N 5755± 5.959e+05

m 0.0000± 0.4982

σ 0.000045± 0.006471

ν 0.074± 2.202

0

p 26.5± 139.4

1p 0.0195± 0.3712

2p 1.48± 30.72

3

p 3.83± -61.04

4p 3.01± 34.41


0.000037±mass = 0.498230

0.000045± = 0.006471σ 64±) in range = 3853

s

0 N(K

S/B = 6.768148

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 173.7 / 110

Prob 0.0001027

N 5755± 5.959e+05

m 0.0000± 0.4982

σ 0.000045± 0.006471

ν 0.074± 2.202

0

p 26.5± 139.4

1p 0.0195± 0.3712

2p 1.48± 30.72

3

p 3.83± -61.04

4p 3.01± 34.41

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

/ ndf 2χ 173.7 / 110

Prob 0.0001027

N 5755± 5.959e+05

m 0.0000± 0.4982

σ 0.000045± 0.006471

ν 0.074± 2.202

0

p 26.5± 139.4

1p 0.0195± 0.3712

2p 1.48± 30.72

3

p 3.83± -61.04

4p 3.01± 34.41


0.000037±mass = 0.498230

0.000045± = 0.006471σ 64±) in range = 3853

s

0 N(K

S/B = 6.768148

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 127.8 / 110

Prob 0.1176

N 5792± 6.204e+05

m 0.0000± 0.4982 σ 0.00005± 0.00702 ν 0.062± 1.959

0p 12.65± 33.75

1

p 0.0245± 0.4046

2p 2.43± 36.54

3

p 5.43± -69.99

4p 3.95± 39.48


0.000038±mass = 0.498249

0.000046± = 0.007020σ 70±) in range = 4347

s

0 N(K

S/B = 9.041011

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 127.8 / 110

Prob 0.1176

N 5792± 6.204e+05

m 0.0000± 0.4982 σ 0.00005± 0.00702 ν 0.062± 1.959

0p 12.65± 33.75

1

p 0.0245± 0.4046

2p 2.43± 36.54

3

p 5.43± -69.99

4p 3.95± 39.48

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700 / ndf 2χ 127.8 / 110

Prob 0.1176

N 5792± 6.204e+05

m 0.0000± 0.4982 σ 0.00005± 0.00702 ν 0.062± 1.959

0p 12.65± 33.75

1

p 0.0245± 0.4046

2p 2.43± 36.54

3

p 5.43± -69.99

4p 3.95± 39.48


0.000038±mass = 0.498249

0.000046± = 0.007020σ 70±) in range = 4347

s

0 N(K

S/B = 9.041011

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600 / ndf 2χ 169.3 / 110

Prob 0.0002439

N 5636± 5.542e+05

m 0.0000± 0.4982

σ 0.000054± 0.008147

ν 0.054± 1.629

0

p 3.28± 10.69

1p 0.042± 0.459

2p 2.39± 36.96

3

p 6.08± -63.37

4p 4.6± 32.2


0.000044±mass = 0.498223

0.000054± = 0.008147σ 78±) in range = 4489

s

0 N(K

S/B = 12.400990

Range = [0.344000,0.700000]

Bin 5

/ ndf 2χ 169.3 / 110

Prob 0.0002439

N 5636± 5.542e+05

m 0.0000± 0.4982

σ 0.000054± 0.008147

ν 0.054± 1.629

0

p 3.28± 10.69

1p 0.042± 0.459

2p 2.39± 36.96

3

p 6.08± -63.37

4p 4.6± 32.2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600 / ndf 2χ 169.3 / 110

Prob 0.0002439

N 5636± 5.542e+05

m 0.0000± 0.4982

σ 0.000054± 0.008147

ν 0.054± 1.629

0

p 3.28± 10.69

1p 0.042± 0.459

2p 2.39± 36.96

3

p 6.08± -63.37

4p 4.6± 32.2


0.000044±mass = 0.498223

0.000054± = 0.008147σ 78±) in range = 4489

s

0 N(K

S/B = 12.400990

Range = [0.344000,0.700000]

Bin 5

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV0

5

10

15

20

25

30

35

40

/ ndf 2χ 141.1 / 104

Prob 0.009124

N 951± 3.962e+04

m 0.0002± 0.4987 σ 0.0003± 0.0112 ν 0.028± 1.013

0p 9.11± 10.47

1

p 0.770± 1.368

2p 19.06± 37.03

3

p 54.90± -74.11

4p 39.60± 42.97


0.000195±mass = 0.498712

0.000294± = 0.011195σ 22±) in range = 424

s

0 N(K

S/B = 22.400183

Range = [0.360000,0.700000]

Bin 6

Figu

reF.14:

Fits

toth

ein

variant

mass

distrib

ution

fromD

jango

Mon

teC

arloin

bin

sof

xT

BF

pfor

the

targethem

isphere

inth

eB

reitFram

e.

164A

PP

EN

DIX

F.

FIT

ST

OM

ASS

DIS

TR

IBU

TIO

NS

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800 / ndf 2χ 142.9 / 110

Prob 0.0192

N 7153± 6.84e+05

m 0.0000± 0.4981

σ 0.000045± 0.006516

ν 0.080± 2.009

0

p 14.1± 127.7

1p 0.0110± 0.3426

2p 0.88± 40.22

3

p 2.4± -84.2

4p 1.99± 49.76


0.000037±mass = 0.498087

0.000045± = 0.006516σ 78±) in range = 4451

s

0 N(K

S/B = 3.324243

Range = [0.344000,0.700000]

Bin 1

/ ndf 2χ 142.9 / 110

Prob 0.0192

N 7153± 6.84e+05

m 0.0000± 0.4981

σ 0.000045± 0.006516

ν 0.080± 2.009

0

p 14.1± 127.7

1p 0.0110± 0.3426

2p 0.88± 40.22

3

p 2.4± -84.2

4p 1.99± 49.76

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800 / ndf 2χ 142.9 / 110

Prob 0.0192

N 7153± 6.84e+05

m 0.0000± 0.4981

σ 0.000045± 0.006516

ν 0.080± 2.009

0

p 14.1± 127.7

1p 0.0110± 0.3426

2p 0.88± 40.22

3

p 2.4± -84.2

4p 1.99± 49.76


0.000037±mass = 0.498087

0.000045± = 0.006516σ 78±) in range = 4451

s

0 N(K

S/B = 3.324243

Range = [0.344000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

/ ndf 2χ 142.6 / 110

Prob 0.01981

N 6835± 7.611e+05

m 0.0000± 0.4981

σ 0.000041± 0.006738

ν 0.049± 1.687

0

p 1043.6± 2198

1p 0.015± 0.474

2p 2.55± 17.81

3

p 4.87± -36.73

4p 3.15± 18.93


0.000034±mass = 0.498123

0.000041± = 0.006738σ 79±) in range = 5111

s

0 N(K

S/B = 6.887736

Range = [0.344000,0.700000]

Bin 2

/ ndf 2χ 142.6 / 110

Prob 0.01981

N 6835± 7.611e+05

m 0.0000± 0.4981

σ 0.000041± 0.006738

ν 0.049± 1.687

0

p 1043.6± 2198

1p 0.015± 0.474

2p 2.55± 17.81

3

p 4.87± -36.73

4p 3.15± 18.93

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

/ ndf 2χ 142.6 / 110

Prob 0.01981

N 6835± 7.611e+05

m 0.0000± 0.4981

σ 0.000041± 0.006738

ν 0.049± 1.687

0

p 1043.6± 2198

1p 0.015± 0.474

2p 2.55± 17.81

3

p 4.87± -36.73

4p 3.15± 18.93


0.000034±mass = 0.498123

0.000041± = 0.006738σ 79±) in range = 5111

s

0 N(K

S/B = 6.887736

Range = [0.344000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

/ ndf 2χ 178.9 / 110

Prob 3.631e-05

N 7962± 8.135e+05

m 0.0000± 0.4981

σ 0.000043± 0.007041

ν 0.038± 1.326

0

p 1.16± 26.55

1p 0.0314± 0.4177

2p 1.10± 34.22

3

p 3.71± -60.04

4p 3.12± 31.12


0.000034±mass = 0.498139

0.000043± = 0.007041σ 95±) in range = 5670

s

0 N(K

S/B = 11.323935

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 178.9 / 110

Prob 3.631e-05

N 7962± 8.135e+05

m 0.0000± 0.4981

σ 0.000043± 0.007041

ν 0.038± 1.326

0

p 1.16± 26.55

1p 0.0314± 0.4177

2p 1.10± 34.22

3

p 3.71± -60.04

4p 3.12± 31.12

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

/ ndf 2χ 178.9 / 110

Prob 3.631e-05

N 7962± 8.135e+05

m 0.0000± 0.4981

σ 0.000043± 0.007041

ν 0.038± 1.326

0

p 1.16± 26.55

1p 0.0314± 0.4177

2p 1.10± 34.22

3

p 3.71± -60.04

4p 3.12± 31.12


0.000034±mass = 0.498139

0.000043± = 0.007041σ 95±) in range = 5670

s

0 N(K

S/B = 11.323935

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600 / ndf 2χ 170.4 / 110

Prob 0.0001973

N 6752± 5.782e+05

m 0.0000± 0.4982

σ 0.000056± 0.007814

ν 0.04± 1.11

0

p 4.90± 10.52

1p 0.0788± 0.7578

2p 3.62± 40.68

3

p 9.02± -71.31

4p 6.60± 36.31


0.000043±mass = 0.498160

0.000056± = 0.007814σ 92±) in range = 4424

s

0 N(K

S/B = 14.298769

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 170.4 / 110

Prob 0.0001973

N 6752± 5.782e+05

m 0.0000± 0.4982

σ 0.000056± 0.007814

ν 0.04± 1.11

0

p 4.90± 10.52

1p 0.0788± 0.7578

2p 3.62± 40.68

3

p 9.02± -71.31

4p 6.60± 36.31

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600 / ndf 2χ 170.4 / 110

Prob 0.0001973

N 6752± 5.782e+05

m 0.0000± 0.4982

σ 0.000056± 0.007814

ν 0.04± 1.11

0

p 4.90± 10.52

1p 0.0788± 0.7578

2p 3.62± 40.68

3

p 9.02± -71.31

4p 6.60± 36.31


0.000043±mass = 0.498160

0.000056± = 0.007814σ 92±) in range = 4424

s

0 N(K

S/B = 14.298769

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

50

100

150

200

250 / ndf 2χ 199 / 109

Prob 3.18e-07

N 2336± 2.461e+05

m 0.0001± 0.4983

σ 0.000097± 0.008789

ν 0.0± 1

0

p 1.60± 4.21

1p 0.200± 1.338

2p 6.50± 54.62

3

p 17.5± -103.1

4p 12.7± 55.7


0.000068±mass = 0.498289

0.000097± = 0.008789σ 43±) in range = 2093

s

0 N(K

S/B = 11.731857

Range = [0.345000,0.700000]

Bin 5

Figu

reF.15:

Fits

toth

ein

variant

mass

distrib

ution

fromD

jango

Mon

teC

arloin

bin

sof

pC

BF

Tfor

the

curren

them

isphere

inth

eB

reitFram

e.

165

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

20

40

60

80

100

120

140

160

180 / ndf 2χ 129.9 / 110

Prob 0.09478

N 3042± 1.44e+05

m 0.0001± 0.4984

σ 0.00009± 0.00558 ν 0.405± 3.474

0p 8.76± 56.09

1

p 0.0175± 0.3517

2p 0.96± 42.26

3

p 2.64± -90.51

4p 2.2± 55.5


0.000075±mass = 0.498413

0.000091± = 0.005580σ 30±) in range = 803

s

0 N(K

S/B = 1.200464

Range = [0.344000,0.700000]

Bin 1

/ ndf 2χ 129.9 / 110

Prob 0.09478

N 3042± 1.44e+05

m 0.0001± 0.4984

σ 0.00009± 0.00558 ν 0.405± 3.474

0p 8.76± 56.09

1

p 0.0175± 0.3517

2p 0.96± 42.26

3

p 2.64± -90.51

4p 2.2± 55.5

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

20

40

60

80

100

120

140

160

180 / ndf 2χ 129.9 / 110

Prob 0.09478

N 3042± 1.44e+05

m 0.0001± 0.4984

σ 0.00009± 0.00558 ν 0.405± 3.474

0p 8.76± 56.09

1

p 0.0175± 0.3517

2p 0.96± 42.26

3

p 2.64± -90.51

4p 2.2± 55.5


0.000075±mass = 0.498413

0.000091± = 0.005580σ 30±) in range = 803

s

0 N(K

S/B = 1.200464

Range = [0.344000,0.700000]

Bin 1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

100

200

300

400

500 / ndf 2χ 120 / 108

Prob 0.2018

N 4951± 4.339e+05

m 0.0000± 0.4983

σ 0.000051± 0.006048

ν 0.160± 3.118

0

p 16.23± 61.39

1p 0.0226± 0.2842

2p 1.69± 40.21

3

p 3.99± -83.14

4p 3.00± 49.17


0.000042±mass = 0.498320

0.000051± = 0.006048σ 52±) in range = 2623

s

0 N(K

S/B = 3.073640

Range = [0.350000,0.700000]

Bin 2

/ ndf 2χ 120 / 108

Prob 0.2018

N 4951± 4.339e+05

m 0.0000± 0.4983

σ 0.000051± 0.006048

ν 0.160± 3.118

0

p 16.23± 61.39

1p 0.0226± 0.2842

2p 1.69± 40.21

3

p 3.99± -83.14

4p 3.00± 49.17

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E

ntrie

s / 3

.000

000

MeV

0

100

200

300

400

500 / ndf 2χ 120 / 108

Prob 0.2018

N 4951± 4.339e+05

m 0.0000± 0.4983

σ 0.000051± 0.006048

ν 0.160± 3.118

0

p 16.23± 61.39

1p 0.0226± 0.2842

2p 1.69± 40.21

3

p 3.99± -83.14

4p 3.00± 49.17


0.000042±mass = 0.498320

0.000051± = 0.006048σ 52±) in range = 2623

s

0 N(K

S/B = 3.073640

Range = [0.350000,0.700000]

Bin 2

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 134.2 / 110

Prob 0.05804

N 6490± 7.997e+05

m 0.0000± 0.4983

σ 0.000039± 0.006396

ν 0.077± 2.549

0

p 18.7± 108.4

1p 0.0178± 0.3818

2p 1.28± 34.24

3

p 3.28± -67.45

4p 2.6± 38.1


0.000032±mass = 0.498325

0.000039± = 0.006396σ 72±) in range = 5112

s

0 N(K

S/B = 6.367626

Range = [0.344000,0.700000]

Bin 3

/ ndf 2χ 134.2 / 110

Prob 0.05804

N 6490± 7.997e+05

m 0.0000± 0.4983

σ 0.000039± 0.006396

ν 0.077± 2.549

0

p 18.7± 108.4

1p 0.0178± 0.3818

2p 1.28± 34.24

3

p 3.28± -67.45

4p 2.6± 38.1

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 134.2 / 110

Prob 0.05804

N 6490± 7.997e+05

m 0.0000± 0.4983

σ 0.000039± 0.006396

ν 0.077± 2.549

0

p 18.7± 108.4

1p 0.0178± 0.3818

2p 1.28± 34.24

3

p 3.28± -67.45

4p 2.6± 38.1


0.000032±mass = 0.498325

0.000039± = 0.006396σ 72±) in range = 5112

s

0 N(K

S/B = 6.367626

Range = [0.344000,0.700000]

Bin 3

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 148 / 110

Prob 0.009118

N 6311± 8.197e+05

m 0.0000± 0.4982

σ 0.000040± 0.007154

ν 0.052± 2.046

0

p 6.40± 30.98

1p 0.0260± 0.4238

2p 1.62± 34.88

3

p 4.2± -63.6

4p 3.26± 34.55


0.000033±mass = 0.498172

0.000040± = 0.007154σ 79±) in range = 5854

s

0 N(K

S/B = 11.865443

Range = [0.344000,0.700000]

Bin 4

/ ndf 2χ 148 / 110

Prob 0.009118

N 6311± 8.197e+05

m 0.0000± 0.4982

σ 0.000040± 0.007154

ν 0.052± 2.046

0

p 6.40± 30.98

1p 0.0260± 0.4238

2p 1.62± 34.88

3

p 4.2± -63.6

4p 3.26± 34.55

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

600

700

800

900 / ndf 2χ 148 / 110

Prob 0.009118

N 6311± 8.197e+05

m 0.0000± 0.4982

σ 0.000040± 0.007154

ν 0.052± 2.046

0

p 6.40± 30.98

1p 0.0260± 0.4238

2p 1.62± 34.88

3

p 4.2± -63.6

4p 3.26± 34.55


0.000033±mass = 0.498172

0.000040± = 0.007154σ 79±) in range = 5854

s

0 N(K

S/B = 11.865443

Range = [0.344000,0.700000]

Bin 4

-) [GeV]π+,πM (

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Ent

ries

/ 3.0

0000

0 M

eV

0

100

200

300

400

500

/ ndf 2χ 191.7 / 110

Prob 2.307e-06

N 5759± 5.401e+05

m 0.0000± 0.4983

σ 0.000059± 0.008621

ν 0.037± 1.202

0

p 6.41± 13.97

1p 0.0906± 0.7555

2p 3.86± 38.42

3

p 9.9± -68.7

4p 7.31± 36.54


0.000046±mass = 0.498260

0.000059± = 0.008621σ 87±) in range = 4572

s

0 N(K

S/B = 17.322227

Range = [0.344000,0.700000]

Bin 5

Figu

reF.16:

Fits

toth

ein

variant

mass

distrib

ution

fromD

jango

Mon

teC

arloin

bin

sof

pT

BF

Tfor

the

targethem

isphere

inth

eB

reitFram

e.

166 APPENDIX F. FITS TO MASS DISTRIBUTIONS

Appendix G

Resumen del trabajo de tesis

Produccion de K0

S a Q2 altas endispersion ep inelastica profunda en H1

En esta tesis se presentan los resultados correspondientes a la primera medicion

de la produccion de mesones K0S a altas Q2 usando los datos colectados con el de-

tector H1 en el laboratorio DESY en Hamburgo, Alemania. Los datos analizados

corresponden al perıodo conocido como HERA II, que comprende los anos 2004-2007

con una luminosidad acumulada de 340 pb−1.

El laboratorio DESY cuenta con un colisionador de partıculas llamado HERA que

acelera protones hasta una energıa de 920 GeV y electrones (o positrones) a energıas

de hasta 27.5 GeV haciendolas colisionar en cuatro puntos estrategicos alrededor de

su circunsferencia, uno de ellos donde se localiza el detector H1 (Figura 3.1).

Este analisis se lleva a cabo despues de seleccionar la muestra de eventos de

dispersion inelastica profunda (DIS por sus siglas en ingles) como se muestra en la

Figura 1.1. Los eventos DIS de corriente neutra se caracterizan por la interaccion

dura de un electron con un proton a traves del intercambio de un boson neutro (γ

o Z0), como resultado se tiene un electron dispersado y un conjunto de partıculas

167

168 APPENDIX G. RESUMEN DEL TRABAJO DE TESIS

hadronicas resultantes del rompimiento del proton, a este conjunto se le denomina

sistema de estados finales hadronicos.

En el detector H1, los eventos DIS a Q2 altas se identifican por la medicion del

electron dispersado usando el calorımetro de Argon lıquido (LAr) mientras que los

estados finales hadronicos son reconstruidos con los detectores centrales de trajectoria

para determinar su carga y momento, y por el calorımetro LAr para la determinacion

de su angulo polar y su energıa. Los eventos DIS se describen usando dos de las

siguientes variables invariantes de Lorentz, el cuadrimomento transferido al cuadrado

del foton Q2, la inelasticidad y y la variable de Bjorken x.

El meson K0S puede ser producido por cuatro mecanismos diferentes, ver Figura 2.3:

a) El proceso de produccion dura del modelo de quarks partonicos (QPM) que

consiste en la interaccion directa de un quark extrano procedente del mar de

quarks en el proton con el foton virtual emitido por el electron.

b) Por fusion de boson gluon (BGF), en el cual un gluon del quark se divide en

un par quark-antiquark extrano y uno de ellos interactua con el electron.

c) Por decaimiento de quarks pesados, producidos primeramente por el proceso

BGF, a quarks extranos.

d) Por el proceso de hadronizacion que se da a partir de la fragmentacion del

campo de color en pares quark-antiquark.

A Q2 altas los cuatro procesos mencionados arriba contribuyen significativamente

a la produccion de K0S .

Los estudios de extraneza son importantes no solo por la medicion de la pro-

duccion, sino tambien porque permiten probar modelos teoricos basados en proce-

sos de hadronizacion y fragmentacion. La comparacion directa de las simulaciones

Monte Carlo con las mediciones del experimento ayudan a mejorar el entendimiento

actual de aspectos de CromoDinamica Cuantica (QCD) ası como a optimizar los

parametros de los programas de simulacion. En particular, para los programas que

169

describen el proceso de hadronizacion por medio del modelo de cuerdas Lund, estas

comparaciones de prediccion-medicion proporcionan una prueba de la universalidad

del factor de supresion de extraneza λs.

En este caso de usan dos programas de simulacion de eventos DIS, Rapgap y

Django, referidos como MEPS y CDM respectivamente en la Figura 1.3. MEPS se

basa en elementos de matriz mas la cascada de partones descritas por medio de las

ecuaciones de evolucion DGLAP que tienen un orden muy fuerte en el momento

transverso kT de los gluones emitidos. CDM tambien usa elementos de matrices pero

la emision de gluones es independiente del momento transverso (no hay orden en kT )

tal cual lo hace el modelo de color dipolar. Ambos modelos tienen una interfase al

modelo Lund para describir la hadronizacion.

El modelo Lund cuenta con tres parametros importantes para describir la pro-

duccion de quarks, el factor de supresion de extraneza λs y los factores de supresion

di-quark, λqq y λsq, que describen la probabilidad relativa de produccion de un par

quark-antiquark extrano con respecto a los pares quark-antiquark ligeros apartir del

campo de color, la probabilidad relativa de creacion de un di-par de quarks con re-

specto a un par de ellos, y la probabilidad de crear di-pares de quarks respecto a

pares. Estos parametros son fijados a los valores proporcionados por la colaboracion

ALEPH: λs = 0.286, λqq = 0.108 y λsq = 0.690. Tanto CDM y MEPS son simulados

con la funcion de densidad de partones (PDF) CTEQ6L.

El meson K0S se identifica por medio de su canal de decaimiento mas frecuente:

K0s → π+π−. Las partıculas hijas, π±, se reconstruyen a partir de trajectorias de

buena calidad medidas en los detectores de trajectoria de H1 que coinciden en un

vertice secundario comun, el cual esta desplazado cierta distancia del vertice primario

de interaccion ep. El espacio de fase elegido para esta tesis se define por 145 < Q2 <

20000 GeV2, 0.2 < y < 0.6, -1.5 < η(K0S) < 1.5 y pT (K0

S) > 0.3 GeV, es decir para

regiones centrales del detector.

La distribucion de masa invariante de los candidatos a K0S seleccionados se aprecia

en la Figura 4.4 de donde se extraen 38154 K0S despues de hacer un ajuste con una


distribucion t-student para describir la senal y la funcion p0(x− 0.344)p1 ∗ exp(p2x+

p3x2 + p4x

3) para el ruido.

La seccion transversal inclusiva medida en la region cinematica accesible es de

σvis = 531 ± 17 (stat)+37−39 (sys) pb donde varias fuentes de error sistematico son

consideradas. La produccion diferencial de K0S en funcion de las variables Q2, x, η

y pT del marco de referencia del laboratorio se presentan en la Figura 6.2 donde la

medicion corresponde a los puntos negros y la comparacion con los modelos CDM

y MEPS con λs = 0.22 y λs = 0.286 respectivamente, se aprecia en la parte baja

de cada grafica. Tambien es posible ver que las mediciones decrecen rapidamente

cuando Q2 y pT toman valores cada vez mas altos, mientras que el comportamiento

en funcion de x y η es mas bien de subida y bajada. Los datos son mejor descritos

en forma y normalizacion por los modelos que tienen el valor de λs = 0.286. Tanto

CDM como MEPS tienen comportamientos similares.

Las secciones trasversales tambien son medidas diferencialmente en el marco de

referencia Breit (Figure 6.3), tanto en la region de corriente (CBF) como en la region

del blanco (TBF), en funcion de la fraccion de momento xp y de momento trasverso

pT . La produccion de K0S decrece a medida que los valores de estas variables son

mayores. Los modelos CDM y MEPS con λs = 0.286 dan buena descripcion de los

resultados en la region de corriente donde el mecanismo de produccion preferido es

el proceso de interaccion dura, mientras que en el hemisferio del blanco los diferentes

modelos permiten observar cierta sensibilidad al parametro λs que es lo esperado

debido a que el proceso de hadronizacion es el que domina en esta region.

Las razon de seccion transversal de los mesones K0S con respecto a la de partıculas

cargadas seleccionadas en el mismo espacio de fase, tambien se mide en el marco del

laboratorio y se presentan en la Figura 6.4, una de las ventajas es la reduccion

de las fuentes de incertidumbre sistematica y por tanto la disminucion del error

sistematico total. La razon de produccion es casi plana en funcion de Q2, hay una

pequena caıda en funcion de x y η, y sube a medida que pT incrementa. Este ultimo

comportamiento se debe a que los mesones llevan mas momento comparado con

171

las partıculas cargadas mas ligeras que en su mayorıa son piones. La forma y la

normalizacion de las mediciones son descritas por los modelos con λs = 0.286.

Las graficas de densidad, que se definen como la razon de la produccion de K0S

con respecto a los eventos DIS seleccionados en la misma region cinematica, se mi-

den diferencialmente en funcion de Q2 y x (Figura 6.5). La razon promedio des-

cansa aproximadamente en 0.4 independientemente de las variables, indicando que

la fraccion de produccion es igual en cualquier region. Los modelos con λs = 0.286

describen los resultados bastante bien en Q2 pero predicen una pequena caıda en x

que no corresponde a la medicion.

La grafica 6.6 muestra los resultados de K0S en funcion de xCBF

p en la region de

corriente para tres regiones distintas de Q2 normalizadas a la seccion trasversal total

de eventos DIS en cada region de Q2. Es posible ver el factor de escalamiento de las

funciones de fragmentacion.

Otros estudios realizados son la comparacion de las secciones trasversales difer-

enciales a modelos CDM con los diferentes PDFs: CTEQ6L, H12000LO y GRVLO,

ver Figura 6.7. Los modelos dan descripciones similares en la forma pero solamente

CTEQ6L y H12000LO describen las mediciones en normalizacion, GRVLO subestima

los resultados debido a la ausencia de contribucion de los quarks pesados encanto c

y belleza b. Resultados similares se obtienen en el marco de referencia Breit.

La contribucion de los sabores de quarks es estudiada usando el programa Rapgap

con λs = 0.286 como es posible ver en la Figuras 6.8 y 6.9. Los quarks ligeros u y d del

proceso de fragmentacion dominan en funcion de todas las variables, ası el mecanismo

de produccion principal de mesones K0S es la hadronizacion. La contribucion de los

quarks pesados c y b son la segunda mas alta en la mayorıa de los bins, estos provienen

del proceso de decaimiento principalmente. La contribucion del quark s permanece

como la mas baja pero llega a ser relevante a valores altos de Q2, x y pT (no olvidar

la escala logarıtmica), mientras que en funcion de η es casi constante. Los procesos

de produccion para s son principalmente la interaccion dura QPM y la fusion de

boson gluon. En funcion de variables del marco de referencia Breit, la contribucion


del quark s a la produccion de K0S llega a ser mas importantes a valores altos de xp y

pT , especialmente en el hemisferio de corriente donde incluso iguala a la contribucion

de quarks pesados.

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Documents

bib-pubdb1.desy.debib-pubdb1.desy.de/record/93879/files/thesisJRuiz.pdf · Acknowledgements I enormously thank my parents, Mr. Agustin Ru´ız y Uex and Mrs. Mar´ıa Eliz-abeth Tabasco