Charm and the Virtual Photon at HERA and a Global Tracking ...€¦ · Charm and the Virtual Photon at HERA and a Global Tracking Trigger for ZEUS Benjamin John West UCL University

Charm and th e V irtual P h oton

at H E R A and a G lobal

Tracking Trigger for ZEUS

Benjamin John West

U C L

University College London

August 2001

Thesis subm itted in fulfillment of the requirem ents for

the degree of D octor of Philosophy in Physics

ProQuest Number: U642447

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A b stract

Previous m easurem ents a t ZEUS have dem onstra ted suppression of photon s tructu re

like effects due to bo th the v irtuality of the photon, and the presence of charm .

In this thesis aspects of these two m easurem ents have been com bined in order to

determ ine w hether these two suppressions are independent.

The m easurem ent was m ade w ith the ZEUS detecto r a t HERA in the kinem atic

region 0 < < 5 • 10^ GeV^ using dijet events containing a D* meson. Events

having two or more je ts w ith large transverse energies were selected using the

longitudinally invariant kr algorithm in the labo ra to ry frame. The dijet cross section

was m easured as a function of the fractional m om entum of the photon partic ipa ting

in the dijet production, , and of

The ratio of low to high cross sections was found not to change significantly w ith

Q^. This is in m arked con trast to previous m easurem ents which did not require a D*,

dem onstrating for the first tim e th a t the observed suppressions of the low cross

section due to non-zero photon v irtuality and due to charm are not independent.

The ratio was also com pared to the predictions of leading-order pQCD. C alculations

which included either a resolved v irtual photon in the D G LAP evolution scheme

or used CCFM evolution gave a b e tte r description of the d a ta th an a D G LA P

calculation w ith no photon structure .

D uring the 2000-2001 shutdow n bo th the H ERA accelerator and ZEUS detector

were upgraded. In order to take advantage of these im provem ents a new “global

tracking trigger” , com bining inform ation from the C entral Tracking D etector and

the newly installed Micro Vertex D etector a t th e Second Level Trigger, has been

developed. T he algorithm is described and its perform ance evaluated. T he event

z vertex resolution is two orders of m agnitude b e tte r th an th a t for the present

algorithm . This will enable fu ture m easurem ents of the cross section ra tio to be

m ade w ith much greater precision.

To my family and friends

“W riting a book is an undertak ing far more horrific th a n I ’d ever imagined. Not

only m ust the w riter come up w ith several tens of thousands of words, not all of

them the same, bu t he or she m ust arrange them in an order th a t makes some sort

of sense to the first tim e reader. I t ’s no use s ta rtin g your book ‘Linford Christie

stepped into the horse-box bem used by th e wall of m ushroom s which stood grinning

a t the back’ if you have no in tention of tak ing these ideas any further. To s ta rt

a book w ith th is sentence, b u t then take your eye off the ball for a m om ent and

end up w riting a tw enty-thousand word guide to Polish war m em orials, deserves the

highest criticism . I t ’s a fau lt th a t took me m any m onths of practice to avoid.

O thers have been less m eticulous. I ’m surely not the only one to have noticed th a t

W ill H u tto n ’s otherw ise adm irably w ritten economics bestseller The State W e ’re In

opens w ith the sentence ‘This book has been carefully graded so th a t you can begin

w ith one or two elem entary dishes yet soon be able to set ou t a full T hai meal

w ith all its unique flavours.’ Nor is there any earth ly explanation other th an sheer

au thorial incom petence for a few stray lines in S tephen H aw king’s A Brief History

of Time which, a t the end of a brilliant explanation of the sym biotic relationship

between quan tum theory and relativity, seductively h in ting a t a unified theory of

gravity, suddenly continue:

Bevin let out a gasp of astonishm ent and playful pleasure a t the

Professor’s rem arks. ‘Ooh boy,’ she yelped, like a cat. ‘Tell it to me one

more tim e, ’cos I ’m on fire, particle m an!’ She rem em bered now their

curiously in terrup ted lovemaking from the previous n ight and resolved

to ham m er the door shut th is tim e.

T he rem aining ninety pages revert to a discussion of partic le /w ave duality w ithin

light emissions.

Consistency is therefore a prerequisite for even the m ost vaguely com petent s tab

a t a book.”

A rm ando lannucci. Facts and Fancies^ 1997

Acknowledgments

Over the last three years I have been fo rtunate enough to work w ith m any excellent

people, w ithout whom th is thesis would not have been possible. For help w ith

my analysis, I would like to thank Jon B utterw orth for his advice and m otivation

throughout; M ark Hayes for teaching me the basics; Leonid G ladilin for his

knowledge of all things heavy flavoured; Jo Cole for her advice on D*s in DIS;

Alex Tapper for his extensive knowledge of DIS and generosity in sharing it; M att

Light wood for his hard work reproducing my analysis; and R ichard H all-W ilton for

continuing where I left off. For all his hard work on the G T T , bo th before and

after I joined the effort, I owe a great deal to M ark S utton . The product of our

collaboration is som ething I th ink we can bo th be proud of. I would also like to

th an k Stew Boogert for m any random physics conversations which helped bo th my

understanding and enthusiasm .

Fortunately, there has been much more to my life th a n ju s t work during my PhD ,

and for th a t I owe m any people thanks. In particu la r I would like to thank Alex

Ferguson for being a good friend and housem ate; A nn W hittle for the tim e we had

together; K ate Evans for listening and being a good friend; B eth Purse for staying

close even when far away; Stew Boogert for being a good cook, host and m ate; Alex

T apper for m any enjoyable hours in bars; Rod W alker for his citrus theory of life;

E laine McLeod for enjoyable conversations, bo th home and abroad; R icardo Gonçalo

for being a great neighbour and friend; Claire Gwenlan for the m any chats; and Jon

B utterw orth for being m ore th a n ju s t a supervisor.

Finally, I would like to th an k my parents for the ir unconditional support and

encouragem ent th roughou t my life.

Contents

I Charm and the virtual photon at HERA 19

1 H ER A and the ZEUS detector 20

1.1 The H ERA a c c e le r a to r ..................................................................................... 20

1 .2 The ZEUS d e t e c to r ............................................................................................ 2 1

1.3 The C entral Tracking D etector (CTD ) ..................................................... 22

1.4 ZEUS c a lo r im e try ....................................................................................................... 23

1.5 The lum inosity m onitor ..................................................................................24

1.6 The ZEUS trigger system .............................................................................. 25

2 QCD and ep Interactions 27

2.1 P ro ton s truc tu re ....................................................................................................... 28

2 .1 .1 T he naive quark parton m odel ............................................................... 30

2.1.2 The QCD improved quark parton m o d e l ............................................31

2.2 Evolution e q u a tio n s ....................................................................................................33

2.2.1 BFK L e v o lu tio n ..............................................................................................34

2.2.2 CCFM e v o l u t i o n .......................................................................................... 35

2.3 Pho ton s t r u c t u r e ....................................................................................................... 36

2.3.1 H ard p h o to p ro d u c t io n ............................................................................... 38

2.3.2 Pho ton s truc tu re fu n c tio n s ........................................................................ 39

2.4 V irtual photon s t r u c t u r e ......................................................................................... 41

2.4.1 Experim ental r e v i e w ................................................................................... 42

2.5 Heavy flavour p ro d u c tio n ......................................................................................... 43

2.5.1 E xperim ental r e v i e w ................................................................................... 44

3 K inem atic reconstruction 47

3.1 R econstruction of y and .................................................................................. 47

3.1.1 E lectron m e t h o d .......................................................................................... 47

9

Acknowledgments

Over the last th ree years I have been fo rtunate enough to work w ith m any excellent

people, w ithou t whom this thesis would not have been possible. For help w ith

my analysis, I would like to thank Jon B u tterw orth for his advice and m otivation

throughout; M ark Hayes for teaching me th e basics; Leonid G ladilin for his

knowledge of all things heavy flavoured; Jo Cole for her advice on D*s in DIS;

Alex Tapper for his extensive knowledge of DIS and generosity in sharing it; M att

Lightwood for his hard work reproducing my analysis; and R ichard H all-W ilton for

continuing where I left off. For all his hard work on the G T T , bo th before and

after I joined the effort, I owe a great deal to M ark Sutton . The product of our

collaboration is som ething I th ink we can bo th be proud of. I would also like to

thank Stew Boogert for m any random physics conversations which helped bo th my

understanding and enthusiasm .

Fortunately, there has been much more to my life th an ju s t work during my PhD ,

and for th a t I owe m any people thanks. In particu la r I would like to thank Alex

Ferguson for being a good friend and housem ate; Ann W hittle for the tim e we had

together; K ate Evans for listening and being a good friend; B eth Purse for staying

close even when far away; Stew Boogert for being a good cook, host and m ate; Alex

T apper for m any enjoyable hours in bars; R od W alker for his citrus theory of life;

E laine McLeod for enjoyable conversations, bo th hom e and abroad; R icardo G onçalo

for being a g reat neighbour and friend; Glaire G wenlan for th e m any chats; and Jon

B utterw orth for being m ore than ju s t a supervisor.

Finally, I would like to th an k my parents for their unconditional support and

encouragem ent th roughou t my life.

Contents

I Charm and the virtual photon at HERA 19

1 H ERA and the ZEUS detector 20

1 .1 The HERA a c c e le r a to r ...............................................................................................20

1 .2 The ZEUS d e t e c to r ......................................................................................................2 1

1.3 The C entral Tracking D etector (CTD) ...............................................................22

1.4 ZEUS c a lo r im e try ......................................................................................................... 23

1.5 The lum inosity m onitor ...........................................................................................24

1.6 The ZEUS trigger system ....................................................................................... 25

2 QCD and ep Interactions 27

2.1 P ro ton s truc tu re .......................................................................................................28

2 .1 .1 The naive quark parton m o d e l ...................................................................30

2.1.2 T he QCD im proved quark parton m o d e l ..............................................31

2.2 Evolution e q u a t io n s ......................................................................................................33

2.2.1 BFK L e v o lu tio n ..............................................................................................34

2.2.2 CCFM e v o l u t i o n .......................................................................................... 35

2.3 P ho ton s t r u c t u r e ......................................................................................................... 36

2.3.1 H ard p h o to p ro d u c t io n ............................................................................... 38

2.3.2 Photon s truc tu re fu n c tio n s ........................................................................ 39

2.4 V irtual photon s t r u c t u r e .........................................................................................41

2.4.1 Experim ental r e v i e w ...................................................................................42

2.5 Heavy flavour p ro d u c tio n .........................................................................................43

2.5.1 E xperim ental r e v i e w ...................................................................................44

3 K inem atic reconstruction 47

3.1 R econstruction of y and ....................................................................................47

3.1.1 E lectron m e t h o d .......................................................................................... 47

9

Contents

3.1.2 Jacquet-B londel m e t h o d .............................................................................48

3.2 Je t re c o n s tru c tio n ..........................................................................................................48

3.2.1 Cone a lg o r i th m ...............................................................................................49

3.2.2 C lustering a l g o r i t h m ....................................................................................50

3.3 r e c o n s t r u c t io n .....................................................................................................51

4 Event selection 53

4.1 Definition of the cross s e c t io n s .................................................................................53

4.2 Online event se lec tio n ...................................................................................................54

4.2.1 F irst Level Trigger (FLT) ......................................................................... 54

4.2.2 Second Level Trigger (SLT) ..................................................................... 55

4.2.3 T hird Level Trigger ( T L T ) .........................................................................55

4.2.4 Efficiency of the trigger c h a i n ............................................................. 56

4.3 Offline event se lec tio n ...................................................................................................58

4.3.1 C o r r e c t io n s .....................................................................................................58

4.3.2 K inem atic s e le c t io n ....................................................................................... 59

4.3.3 D* re c o n s tru c tio n ...........................................................................................60

4.4 Background E s tim a tio n ............................................................................................... 61

5 Event description and correction 63

5.1 M onte Carlo s im u la tio n ............................................................................................... 63

5.1.1 M onte C arlo s a m p le s ....................................................................................63

5.2 Com parison of d a ta and M onte C a r l o ...................................................................64

5.3 Acceptance correction ............................................................................................... 67

5.4 S tudy of system atic uncertain ties on the r a t i o ............................................... 70

5.4.1 U ncertain ties arising from calorim eter q u a n t i t ie s .............................. 70

5.4.2 U ncertain ties arising from tracking quantities ..................................71

5.4.3 U ncertain ties arising from the M onte Carlo description . . . . 72

5.4.4 In itia l s ta te r a d ia t io n ....................................................................................73

6 R esults and D iscussion 75

6 .1 Com parison to LO pQ CD p re d ic tio n s ...................................................................75

6 .2 Im plications for ...................................................................................................... 77

6.3 Com parison to ra tio w ithou t a D* tag ...............................................................78

6.4 Je t production in DIS and the Y p f r a m e ........................................................... 81

10

Contents

II A global tracking trigger for ZEUS 83

7 The upgrades to H ERA and the ZEUS detector 84

7.1 In tro d u c t io n ...................................................................................................................84

7.2 H E R A ............................................................................................................................. 85

7.3 Straw Tube Tracker ( S T T ) .......................................................................................8 6

7.4 Micro Vertex D etector ( M V D ) ............................................................................... 87

7.4.1 Barrel s e c t i o n ...................................................................................................8 8

7.4.2 Forward s e c t io n ............................................................................................... 90

8 The G TT algorithm 91

8.1 E xisting C T D - S L T .....................................................................................................91

8.1.1 Segment f in d in g ............................................................................................... 91

8.1.2 Vector h it f in d in g ............................................................................................93

8.1.3 Track f i n d i n g ...................................................................................................93

8.1.4 Event vertex determ ination ...................................................................... 95

8.2 M otivation for a G T T ..............................................................................................96

8.2.1 Im provem ents to the C T D - S L T ............................................................... 96

8.2.2 Heavy fiavour tagging a t the S L T ............................................................97

8.3 T he G T T algorithm ................................................................................................. 97

8.3.1 Segment f in d in g ............................................................................................... 98

8.3.2 Axial track f i n d i n g ........................................................................................ 98

8.3.3 z track f in d in g .................................................................................................100

8.3.4 Event vertex determ ination .................................................................... 106

8.4 Future w o r k .................................................................................................................107

8.4.1 Second pass of z-track f in d i n g .................................................................108

8.4.2 Dealing w ith non-ideal w a f e r s .................................................................108

8.4.3 Secondary vertex f in d in g ........................................................................... 109

9 Perform ance of the G TT 111

9.1 MVD sim ulation ...................................................................................................... I l l

9.2 Event s a m p l e ..............................................................................................................1 1 2

9.3 Track r e s o lu t io n s ...................................................................................................... 116

9.3.1 p t resolution .................................................................................................117

9.3.2 (j) r e s o lu t io n .................................................................................................... 118

11

Contents

9.3.3 77 r e s o lu t io n .................................................................................................. 119

9.3.4 ztrack r e s o lu t io n ........................................................................................... 119

9.4 Track e ff ic ie n c y ........................................................................................................ 120

9.5 Event v e r te x ................................................................................................................122

9.6 L a t e n c y ...................................................................................................................... 123

III Summary 125

A M onte Carlo event generators 129

A .l H E R W I G ...................................................................................................................130

A.2 P Y T H IA ...................................................................................................................... 131

A.3 A R O M A ...................................................................................................................... 131

A.4 CASCADE .................................................................................................................131

B D erivation of Errors 133

B .l P u r i t y ..........................................................................................................................133

B .2 Efficiency ...................................................................................................................134

B.3 Correction f a c t o r .....................................................................................................134

C M aths of the GTT algorithm 136

C .l C onstrained r-cj) track f i t ...................................................................................... 136

C .2 U nconstrained r-cf) track f i t ...................................................................................137

C.3 Intersection of an axial track w ith a stereo wire in z - s ............................. 138

R eferences 141

12

List of Figures

1.1 The HERA accelerator chain (left) and delivered lum inosity from1992-2000 (righ t)............................................................................................................20

1 .2 Overview of the ZEUS detec to r.................................................................................21

1.3 x-y view of the CTD showing the wire layout (left) and a C TD driftcell (righ t).........................................................................................................................2 2

1.4 Cut-away view of an FCAL m odule........................................................................ 23

1.5 The Lum inosity M onito r..............................................................................................24

1.6 The ZEUS d a ta acquisition and trigger system .................................................. 25

2 .1 K inem atics of a deep inelastic scattering event...................................................28

2 .2 The NC and CC cross sections as a function of m easured a t HERA. 29

2.3 vs. for fixed x. The fixed-target results from NMC, BCDMS,and E665 and the ZEUS NLO QCD fit are also show n.................................. 32

2.4 Schem atic representation of the applicability of various evolutionequations across the {x, Q^) p lane .......................................................................... 34

2.5 Schem atic representation of the gluon ladder and quark box E ................... 35

2.6 T he to ta l photon-proton cross section....................................................................37

2.7 Exam ples of leading-order processes resulting in two jets; (a) QCD C om pton, (b) boson gluon fusion, (c) fiavour excitation from the proton, (d) gluon gluon fusion, (e) and (f) fiavour excitation fromthe pho to n ........................................................................................................................ 38

2.8 The d istribu tion in dijet events for d a ta (black dots) com pared w ith HERW IG w ith and w ithou t M PI (solid line and do tted line),and PY TH IA w ith M PI (dashed line) M onte Carlo genera to rs ...................39

2.9 Feynm an diagram for e j d iagram w ith a v irtual photon , 7 *, probingan on-shell photon, 7 (left). Sum m ary of current results on (right). 40

2.10 Triple differential cross section a / dx^^dQi^ a s a function of

^obs different regions in and F ^ (le ft) . T he ra tio of cross sections R = cr(T°^^ < 0.75)/cr(T°^^ > 0.75) as a function of(righ t).................................................................................................................................42

13

Figures

2 .1 1 D ifferential cross sections for D* p roduction in DIS. T he open (shaded) band shows the result of an NLO QCD calculation using Peterson (R A PG A P extracted) fragm entation (left). as afunction of x and (righ t)...................................................................................... 45

2.12 The differential cross section da/dri^* for photoproduction com pared to several NLO calculations (left). T he differential cross section da/dx^^ for dijets w ith an associated D* (right) com pared to LO (upper) and NLO (lower) predic tions..............................................................46

3.1 y and resolutions using the electron and Jacquet Blondel m ethods. 49

3.2 Je t Et and rj resolutions for GAL cell je ts using the KTGLUS algorithm . 51

3.3 resolution in photoproduction and D IS........................................................ 52

4.1 TLT Efficiency for d a ta (points) and M onte Carlo (bands).................... 57

4.2 Box cut applied to the scattered electron .......................................................59

4.3 H adron level in GeV for events passing all detector level cuts. . . 60

4.4 Signals for the 1996-2000 d a ta , the line shows the resu lt of anunbinned fit to the signal and the h istogram the wrong charge background estim ate .............................................................................................. 61

5.1 Com parison of d a ta (points) and PY T H IA M onte Carlo (histogram )^obs d istribu tions in P H P and DIS events..................................................... 65

5.2 C om parison of d a ta (points) and M onte Carlo (histogram ) for event,je t and D* properties of the events entering the cross section m easurem ent............................................................................................................. 6 6

5.3 Purity , efficiency and correction factor shown for th e unfolding procedure as a function of x^^ for each region............................................6 8

5.4 Low and high cross sections for events w ith a D* as a functionof Q^. E rrors are sta tistica l only.............................................................................. 69

5.5 R atio of low to high x^^ cross sections for events w ith a D* as a function of Q^. E rrors are s ta tis tica l only............................................................ 70

5.6 System atic uncertain ties due to the kinem atic cuts as a function of 3:°^ . T he shaded band shows th e s ta tis tica l error on the central ra tio value.................................................................................................................................... 71

5.7 System atic uncertain ties due to the D* as a function of . The shaded band shows the s ta tis tica l error on the central ra tio value. . . 72

5.8 System atic U ncertainties due to the M onte Carlo as a function of. T he shaded band shows th e s ta tis tica l error on the central ra tio

value.................................................................................................................................... 73

6.1 R atio of low to high cross sections for events w ith a D* com pared to the LO pQ CD predictions of HERW IG using the S aS lD P D F (upper), and AROM A and CASCAD E (lower).................................................. 76

14

Figures

6 .2 Predicted ratio of low to high for events containing a D*, w ith7and w ithout D* cuts (left) for H E R W IG /SaS ID . M onte Carlo hadron level p t {D*) and ri[D*) d istribu tions predicted by H ER W IG /SaS ID for events passing all other hadron level cuts (r ig h t).................................. 79

6.3 R atio of low to high events w ith a D* com pared to the7predictions of the SaS lD photon stru c tu re function for the ra tio w ithou t a D* tag. The upper edge of the band represents the expected ra tio for the full D* phase space.............................................................................. 80

6.4 R atio of low to high for events containing a D* in the LAB and 7 *p fram es (left). Change in r]{D*) and 77-̂ *̂ when boosting to the Y p fram e (righ t).................................................................................................................... 82

7.1 An exploded view of the Straw Tube Tracker......................................................8 6

7.2 A cross section of an STT layer.................................................................................87

7.3 A cross sectional view of the M V D .......................................................................... 87

7.4 3D and 2D views of the barrel section of the M V D ...........................................8 8

7.5 Top view of a ladder...................................................................................................... 8 8

7.6 Side view of a m odule................................................................................................... 89

7.7 Schem atic diagram of a half m odule........................................................................89

7.8 P a rtia l cross section of a sensor w ith two readout s tr ip s .................................89

7.9 3D and 2D views of the forward section of the M V D .......................................90

8 .1 Axial segment ghost am biguity..................................................................................92

8.2 P a tte rn recognition in a strip detecto r w ith two h its ........................................97

8.3 Stereo segment ghost am biguity................................................................................ 98

8.4 Schem atic diagram of the r-4> track finding..........................................................99

8.5 T he (j) residuals of the closest M VD hits to ex trapo la ted track duringthe MVD r-cf) m atching stage.................................................................................. 100

8 .6 Schem atic diagram of the z-s track finding........................................................ 101

8.7 T he d istribu tion of %^/nseg for superlayer 9, 7, 5 and 3 tracks............... 102

8 .8 The z-segm ent residuals of the segm ent end points w ith respect tothe ex trapo lated track position during the stereo segm ent finding.From the top: superlayer 5, 7 and 9 tracks; from left to right: th e ex trapo la ted positions in superlayer 2 , 4 and 6 . The dashed (solid) histogram shows th e residuals (w ithout) using the MVD wafer guide position ............................................................................................................................ 104

8.9 T he z residuals of th e closest M VD h its to ex trapo la ted track duringthe MVD z m atching stage for superlayer 9 tracks........................................ 105

8.10 Secondary vertex displacem ents and im pact param eters for D mesons(histogram ) and D mesons whose daughters have p > 0.3 GeV and|?7|

Figures

9.1 Pt , t], Ztrack and m ultiplicity d istribu tions of the M onte Carlo used toevaluate th e G T T ........................................................................................................112

9.2 Event displays showing the offline (upper) and G T T (lower) tracksfor the sam e MG event.............................................................................................. 114

9.3 Event displays showing the offline (upper) and G T T (lower) tracksfor a busy MG event...................................................................................................115

9.4 Pt , ÿ, rj, and Ztrack residuals for G T T track s .....................................................116

9.5 Pt resolution as a function of p t , p, ztrack, and event m ultiplicity forG T T and offline tracks .............................................................................................. 117

9.6 0 resolution as a function o fp ^ , P, Ztrack, and event m ultiplicity forG T T and offline tracks .............................................................................................. 118

9.7 p resolution as a function of p, Ztrack, and event m ultiplicity for G T T and offline tracks .............................................................................................. 119

9.8 Ztrack icsolution as a function of p t , p, Ztrack, and event m ultiplicityfor G T T and offline tracks....................................................................................... 120

9.9 Track finding efficiency as a function of p t , p, Ztrack, and eventm ultiplicity for G T T and offline tracks............................................................... 121

9.10 Track finding efficiency as a function of p t , p, ztrack, and eventm ultiplicity for axial G T T tracks and full G T T tracks w ith andw ithout a second pass................................................................................................ 1 2 1

9.11 G T T and offline event Zytx resolution and efficiency..................................... 122

9.12 The latency of the GTD only algorithm on d a ta after a GELT accept taken during the 2000 running period (left) and of the G TD +M V D algorithm on dijet M onte Garlo (righ t)............................................................... 124

9.13 A real cosmic event reconstructed by the G T T using GTD and MVD inform ation in A ugust 2001................................................................................... 127

9.14 G T T (GTD Only) event vertex d istribu tion for real d a ta after GELTand TLT accepts. The beam -gas con tribu tion can clearly be seen. . . 127

16

List of Tables

5.1 G enerated MC subsam ples.................................................................................. 64

5.2 LO -D IR and LO-RES norm alisations for PY TH IA and HERW IG. . . 65

9.1 Table showing p t , , p, and Ztrack resolutions for CTD-SLT, G T T ,and offline tracks...................................................................................................... 116

9.2 Event Zytx resolution for GTD-SLT, G T T , and offline algorithm s. . . . 123

17

Part I

Charm and the virtual photon atHERA

19

Chapter 1

HERA and the ZEUS detector

1.1 The H E R A accelerator

H E RA

W est Hall (HERA-B!

OOBIS

South Hall (ZEUS!

HERA luminosity 1992 - 2000

2000

e•a

C hapter 1 1.2 The ZEUS detector

are passed to the PETR A accelerator, where they are accelerated to 40 GeV and

injected into the HERA proton machine. This process continues until HERA is

filled w ith 210 bunches, which are then accelerated to the HERA operation proton

energy^ using conventional radio frequency cavities. The proton beam is focused

and guided by superconducting quadrupole and dipole magnets.

Lepton injection commences with LINACS’s I and II which accelerate lepton beam s

to 220 and 450 MeV respectively. These are then transferred to the DESY II

synchrotron and accelerated to 7.5 GeV before being injected into the PETR A II

storage ring in bunches w ith 96 ns spacing. The beam is then accelerated to 14 GeV

and injected into the HERA lepton machine. After it is filled with 210 bunches the

beam is accelerated to the operating energy of 27.52 GeV, using bo th conventional

and superconducting cavities.

1.2 T he ZEUS detector

OverView o f t h e Z E U S D E J E C I O R 2 0 0 0 ( I o p v i e w c u t

- 1 0 m

5m 0 -5mFigure 1.2; Overview of the ZEUS detector.

The ZEUS detector, shown in Figure 1 .2 , is a general purpose m agnetic detector,

w ith nearly herm etic calorim etric coverage. A detailed description of the ZEUS

detector can be found elsewhere [1]. A brief outline of the com ponents which are

most relevant for th is analysis is given below.

1820 GeV from 1992-1997 and 920 GeV from 1998-2000.

21

Chapter 1 1.3 The Central Tracking Detector (CTD)

f ie ld w ire

sh a p e r w ire

— g u a rd w ire

— g ro u n d w ire

Figure 1.3; x-y view of the CTD showing the wire layout (left) and a CTD drift cell (riyht).

1.3 The Central Tracking D etector (C T D )

The CTD [2] is a cyliiiclrical drift chamber, which operates in a m agnetic field of

1.43T, provided by a thin superconducting coil. The CTD consists 72 cylindrical

drift cham ber layers, organised in 9 superlayers, covering the polar angle range 15°-

164°. A superlayer contains between 32 and 96 drift cells, each com prising eight

sense wires oriented in a plane a t 45° to the radial line from the cham ber axis. The

drift field is a t a Lorentz angle of 45° to the radial axis so th a t the drift electrons

follow radially transverse paths which is im portan t in left-right am biguity breaking.

W ires in the odd numbered “axial” superlayers run parallel to the z axis^, whereas

wires in the even numbered “stereo” superlayers are at a small stereo angle (~ ±5°),

allowing both r-cf) and z coordinates to be accurately m easured. The nominal

resolution for full length tracks in the CTD is 180 y m in r — ( f ) and % 2 mm in

z. The first three axial layers are also instrum ented with a z-by-tim ing system

which estim ates the position of a h it along a wire from the pulse arrival times at

each end of the chamber. The resolution using this m ethod is ~ 4 cm and it is

predom inantly used for trigger purposes.

The transverse m om entum resolution for full length tracks is (j (p t ) / pt = 0.0058pr@

0.0065 © 0.0014/pT, w ith p r in GeV [3].

^The ZEUS coordinate system is a right-handed Cartesian system, with the z axis pointing in the proton beam direction, referred to as “forward direction” , and the x axis pointing left towards the centre of HERA. The coordinate origin is at the nominal interaction point.

22

Chapter 1 1.4 ZEUS calorimetry

1.4 ZEUS calorim etry

te n s io n s tra p ^ |

The high-resolution iiranium -scintillator calorim eter (CAL) [4] consists of three

parts: the forward (FCAL), the barrel (BCAL) and the rear (RCAL) calorimeters.

Each part is subdivided transversely into towers and longitudinally into one

electrom agnetic section (EMC) and either one (in RCAL) or two (in BCAL and

ECAL) hadronic sections (HAC). The smallest subdivision of the calorim eter is

called a cell. Each HAC cell is approxim ately 2 0 x 2 0 cm and each EMC cell is

approxim ately 5x20 cm (in BCAL and FCAL) or 10x20 cm (in RCAL). The readout

is performed by two photom ultipliers (coupled to the scintillator by wavelength

shifters) per cell; the pair ensuring the measurement to be independent of the im pact

point of the particles. A typical FCAL module w ith EM C and HAC divisions can

be seen in Figure 1.4.

The EMC is the inner section of the tower,

with two hadronic sections (HACl and HAC2 )

outside this. The a lternating layers of De-

])leted Uranium and scintillator can also be seen.

The unequal res])onse, due to hadronic showers

l)roducing fewer photons than electrom agnetic

showers for a particle of the same energy, is com

pensated by the uranium , which absorbs neu

trons from the hadronic shower and em its pho

tons which can then be detected by the photo

m ultipliers. By choosing a suital)le thickness of

uranium , the same num ber of photons are pro

duced for hadronic and electrom agnetic showers

of the same energy. This is im portan t in the re

construction of je ts which are composed of both

electrom agnetic and hadronic com ponents in an

unknown proportion. The CAL energy resolu

tions, as measured under test beam conditions,

are a { E ) / E = 0 .18 \ /Ê for electrons and a { E ) / E = 0 .35 \Æ ’ for hadrons {E in GeV).

Associated w ith the CAL are several subcom ponents, designed to improve the energy

resolution or particle identification properties of the calorim eter, two of which are

relevant to this analvsis.

P A R T IC L E

HAC low er

Silicon d e te c to r

sc in tilla to r p la te

ZEUS FCAL MODULE

Figure 1.4: Cut-away view of an FCAL module.

23

Chapter 1 1.5 The luminosity monitor

Presampler

The Presam pler [5] is a th in segmented layer of scin tillator on the inner face of

the calorim eter. This can be used to estim ate the am ount of showering, and hence

energy loss, th a t a particle has undergone while passing through the dead m aterial

before the CAL.

SRTD

The Small-angle Rear Tracking D etector (SRTD) [6 ], is designed to measure

electrons scattered at small angles and improve the m easurem ent of their position

and energy. The SRTD is located on the face of the RCAL, around the beam pipe,

covering the polar angle region 162°-170°. This region is particularly im portan t

because it is the region in which most DIS electrons are scattered. The SRTD

consists of two layers of hnely segmented silicon strips, resulting in a tracking

resolution of about 3mm, compared to 1cm in the calorim eter. The SRTD also

provides a m easurem ent of the am ount of showering before the CAL wliich can be

used to correct the energy obtained from the calorim eter.

1.5 The lum inosity m onitor

Luminosity Monitor

BU

# 0BU BU BU

10 20

lumi-e

lumi-Y

30 40 50 60 70 80 90 100 110(m )

Figure 1.5: The Luminosity Monitor.

Tlie lum inosity is m easured using the rate of B ethe-H eitler photons, ep -4- epy,

where the 7 is em itted by the electron at a very low angle to the incident electron

direction in negative z. The cross section for th is process is very high and can

be calculated to w ithin 0.5%. The m easurem ent of the small angle electron and

24

Chapter 1 1.6 The ZEUS trigger system

Event Builder

TLTProcessor

TLTProcessor

LocalSLT

TLTProcessor

LocalFLT

GSLTDistribution

GFLT

GSLT

ComponentProcessor

ComponentProcessor

ComponentProcessor

ComponentProcessor

Optical Link / Mass Storage

Figure 1 .6 : The ZEUS data acquisition and trigger system.

photon is performed by two se])arate detectors. The photon detector is situated

close to the beam pipe between 104 and 107 m from the in teraction point, in the

electron direction. The electron detector is situated 34 m from the interaction point.

Both detectors are based on lead-scintilla tor sandwich calorim eters w ith an energy

resolution of a { E ) / E = 0 .18 \Æ .

1.6 The ZEUS trigger system

The nominal bunch crossing ra te of the HERA accelerator is ~ 10 MHz which poses

challenges for the D ata AcQuisition (DAQ) and trigger systems. The interaction

ra te is dom inated by interactions between the proton beam and residual gas, “beam

gas” , which contributes about lO-lOOkHz, whilst the rate w ritten to tape for ep

interactions is between a few and 10 Hz.

25

Chapter 1 1.6 The ZEUS trigger system

To reduce the rate to less than ~ 1 0 Hz w hilst efficiently selecting ep events, ZEUS

uses a th ree stage trigger system [7] shown in Figure 1.6.

The ra te is initially reduced to ~ 1 kHz by the F irs t Level Trigger (FLT) which is

a hardw are based trigger. Each com ponent used a t th e FLT has its own FLT and

stores the d a ta in a pipeline aw aiting a decision. The decision is m ade w ith in ~ 2 /zs

of the bunch crossing and passed onto the Global F irs t Level Trigger (GFLT) which

then makes a final decision in 4.4 /is, passing the decision back to the com ponent

readout.

Events which pass the FLT proceed onto the Second Level Trigger (SLT). The SLT

is a software based trigger run on a network of transpu ters, designed to reduce the

ra te by approxim ately a factor of ten. Analogously to the FLT, each com ponent

can have its own SLT, which passes decisions onto the G lobal Second Level Trigger

(GSLT).

Each com ponent then passes the filtered events to an event builder which fills the

d a ta s tru c tu re for the T h ird Level Trigger (TLT). The TLT runs a crude version

of the full reconstruction software and is able to make decisions concerning global

event properties, je t properties and event kinem atics. The event ra te is now reduced

to a m anageable ~ 1 Hz. The final stage is to transfer the events by an optical fibre

link to storage for processing by the full ZEUS reconstruction software a t a la ter

date.

26

Chapter 2

QCD and ep Interactions

T he in teractions of quarks and gluons are described by Q uantum Chrom odynam ics

(Q CD), a non-abelian gauge theory based on the SU(3) colour sym m etry group. The

quarks, each in three colours, in teract by the exchange of electrically neu tra l vector

bosons, gluons, which form a colour octet. The gluons are no t colour neu tra l and

thus they themselves in teract strongly. A consequence of th is p roperty is asym ptotic

freedom , which states th a t the in teraction streng th of two coloured objects decreases

th e shorter the distance between them . The effective strong coupling constant

then depends on the scale a t which the QCD process occurs. T he leading-order

solution of the renorm alisation group equation gives

= /3oln(QVA2) ’ (2.1)

where denotes the scale a t which as is probed and A is a QCD cutoff param eter.

T he param eter is related to the num ber of quark flavors in the theory, Nf, by

^ 0 = 11 — 0 ^ / - (2 -2 )

Since the known num ber of flavors is six, /3o > 0, the coupling constan t becomes

sm aller the larger the scale Q^. The p roperty of asym ptotic freedom has been proven

rigorously and allows predictions for the properties of strong in teractions to be m ade

in the p ertu rba tive QCD (pQ CD) regime, in which is sm all. One such exam ple

is the production of jets^ in annihilation a t LEP in which ~ M |. A t lower

scales as becomes large m aking pertu rba tive calculations unreliable and accurate

^The produced quarks and gluons cannot be observed directly due to the phenomena known as “colour confinement”. Instead a spray of hadrons, called a jet, emerges in the approximate direction of each parton.

27

C hapter 2 2.1 Proton structure

predictions cannot be made. For example, the d istribu tion of the “partons” bound

in hadrons, cannot be calculated from first principles.

QCD has been tested in dep th in the pertu rba tive regim e and describes the d a ta

very well [8 ]. However, because the observables are based on hadrons ra th e r th an the

partons to which pertu rba tive calculations apply the precision achieved in testing

QCD is lower th an in the case of electroweak in teractions and a detailed experim ental

knowledge of the struc tu re of hadrons is essential.

2.1 P roton structure

l { k )

^ V»(


IÎ

10

10

10

10

10

10

10

10

* HI e^p NC 94-00 prelim.A H I e p NC□ ZEUS e^p NC 99-00 prelim, o ZEUS e p NC 98-99 prelim.

-- SM e^p NC (CTEQ5D)— SM e p NC (CTEQ5D)


F2 is th e generalised stru c tu re function of 7 and exchange, F l is the longitudinal

s tru c tu re function, and F 3 is the parity violating te rm arising from exchange.

Since F 3 is small for « M | it is neglected in all fu rth er discussions here. A

detailed derivation of all these term s is given, for exam ple, in [9].

2.1.1 The naive quark parton model

The form of the cross sections given above is com pletely general, all the physics

detail is contained in the s truc tu re functions. A priori these m ight be expected

to be com plicated functions of p and reflecting the com plexity of the inelastic

scattering process. However, in 1969, Bjorken predicted th a t in the deep inelastic

region^ the structu re functions should “scale” , i.e. becom e functions not of and

1/ independently bu t only of the ir ratio Q'^/u. T his predicted scaling was confirmed

by results from SLAC [1 0 ].

Feynm an gave an in tu itive explanation of B jorken’s argum ents in his parton

m odel [1 1 ], in which the p ro ton is assum ed to be com posed of point-like objects,

called partons. The inelastic scattering of the lepton off th e p ro ton is then described

as the elastic scattering of the lepton off a parto n within th e proton. The ep

cross section is then given by the incoherent sum of the electron-parton scattering

processes.

If a parton of mass m , carrying a fraction, of the to ta l p ro ton m om entum is

struck, conservation of four-m om entum implies ^

t)^rn^ = {^p + q f = V - g

T he Bjorken scaling variable, x, then has a simple in te rp re ta tio n as the fraction of

the longitudinal pro ton m om entum , carried by th e p arton in the hard scatter.

W ith in the parton m odel the s truc tu re functions are given by

(2 .12)i

f i W = (2.13)

u 00 but f v finite.^This is in the infinite momentum frame of the proton, where the partons have no transverse

momentum and the masses can be neglected.

30


where are the parto n charges and fi{x) are the parto n density functions which

can be in terpreted as th e probability of finding a p arton i w ith m om entum fraction

X in the proton. F2 and Fi are connected by the C allan-G ross relation

2 j;F iW (2.14)

which is a direct consequence of the assum ption th a t partons are massless, sp in-1 / 2 ,

non-in teracting particles and implies th a t Fl is zero.

T hrough m easurem ents a t SLAC and in u N scattering [12], these partons were

associated w ith the quarks of the Gell-M ann and Zweig and the m odel becam e the

quark parton model (Q PM ).

2.1.2 The QCD improved quark parton model

If the proton consisted solely of charged quarks the sum of the ir m om enta would be

equal to th a t of the p ro ton , i.e.

1

f dxf i {x)x = 1. (2.15)* 0

However, experim entally th is value was found to be % 0.5 [13]. This im plies th a t

there are also electrically neu tra l particles w ith in the p ro ton which carry ~ 50%

of its m om entum . These particles are identified w ith gluons, the gauge bosons of

QCD. D irect evidence for the existence of these gluons, was provided in 1979 via

the observation of 3-jet events in e+e" annih ilation a t DESY [14].

In th is QCD im proved Q PM , the assum ption th a t the transverse m om entum of the

partons is zero, in the infinite m om entum frame, no longer holds. A quark can em it

a gluon and acquire a large transverse m om entum kr w ith probability proportional

to CKg dk ‘̂ /k^ a t large kx- This integral extends up to the kinem atic lim it, ^

and gives rise to con tribu tions proportional to CKg log which break scaling. This

was experim entally confirm ed by the observation of a logarithm ic dependence on

of F2 ( x ,Q ‘̂ ) and was one of the first m ajor successes of p ertu rba tive QCD.

Figure 2.3 shows th e la tes t m easurem ent of the x and dependence of F2 from

ZEUS, clearly showing these scaling violations [15]. A t large values of x, where the

valence quarks dom inate, F2 (and hence the quark density) can be seen to fall w ith

increasing At low x, where the num ber of “sea” quarks and gluons is larger, F2

is clearly seen to increase w ith Q^.

31

Chapter 2 2.1 Proton structure

ZEUS

CJDO

0

x = 6 .3 E -0 5 x = 0 .0 0 0 1 0 2

(= 0 .000161x = 0 .0 0 0 2 5 3

x = 0 .0004 x = 0 .0005

(= 0 .0 0 0 6 3 2 x = 0 .0 0 0 8

.00102 .0013

1.00161

0.0021 .00253

0 .0032

x = 0 .005

• ZEUS 96/97 A Fixed Target - NLO QCD Fit

x = 0 .008

x = 0 .0 1 3

x = 0.021

x = 0 .0 3 2

l _ x = 0 .05

x= 0 .0 8

x = 0 .13

*- i , > j i x = 0 .18

x = 0 .25

x = 0.4

x = 0 .65

1 0 1 0 ̂ 1 0 ̂ l o ' ' , l o C(GeV^)

Figure 2.3: vs. for fixed x. The fixed-target results from NMC, BCDMS,and E665 and the ZEUS NLO QCD fit are also shown.

32

Chapter 2 2.2 Evolution equations

2.2 E volution equations

The factorisation theorem of collinear (mass) singularities [16] sta tes th a t, in

a general hard collision (i.e. a scattering process involving a large transferred

m om entum )$> A^) of incoming hadrons, all long-distance (non-perturbative)

effects can be factorised into universal (process-independent) parton densities thus

leading to a pertu rbatively calculable dependence on the hard scattering scale

called parton evolution. This dependence arises because a quark seen a t a scale

Ql as carrying a fraction Xq of the proton m om entum can be resolved into more

quarks and gluons, having x < xq, when the scale is increased.

One set of p arton evolution equations derived on the basis of the collinear

factorisation theorem are the D okshitzer-G ribov-Lipatov-A ltarelli-Parisi (D G LA P)

evolution equations [17]. The D GLAP equations describe the way the quark q and

gluon g m om entum distribu tions in a hadron evolve w ith the scale of the in teraction

Q '.

dqi(x ,Q ‘̂ )dlogQ^

dg{x ,Q ‘̂ )dlogQ^

^ f dy

yX

1

^ f dy2 % y V

+ givi Q )Pqg -X

Y ^ g i { y , Q ^ ) Pgq ( - ) +9{y,Q^)Pgg ( - )

(2,16)

,{2.17)

where qi{x,Q^) is the quark density function, for each quark flavour i and g { x , Q ‘̂ )

is the gluon density function. The “sp litting functions” Pjk represent the

probability of a parton k of m om entum fraction y em itting a parton j of m om entum

fraction x. This probability will depend on the num ber of splittings allowed in

the approxim ation. Given a specific factorisation and renorm alisation scheme, the

sp litting functions Pjk are obtained in QCD by p ertu rba tive expansion in CKg,

y j \ y J 27t \ y

The truncation after the first two term s in th e expansion defines the next-to-

leading order (NLO) D G LA P evolution. This approach assumes th a t the dom inant

contribution to the evolution comes from subsequent parton emissions which are

strongly ordered in transverse m om enta the largest corresponding to the p arton

in teracting w ith the probe.

At small X, higher order contributions to the sp litting functions of the form

(2.18)

33


High density region

CCFM

Unconventional DGLAP Modified BFKL

DGLAP

£ n

Figure 2.4: Schematic representation of the applicability of various evolutionequations across the (x, Q^) plane.

P (n) ~ —InX

n —1X

will be enhanced, spoiling the convergence of (2.18). T hus th e conventional

D G LAP equations may be inadequate a t low x and m ust e ither be modified or an

a lternative set of evolution equations used. Figure 2.4 shows th e expected regions of

applicability of various alternatives across the (x, plane. T he BFK L and CCFM

evolution equations, which are based on a generalisation of th e collinear factorisation

theorem called kr factorisation [18] will now be discussed.

2.2.1 BFKL evolution

The B alitsky-Fadin-K uraev-L ipatov (BFKL) [19] evolution equation allows the

resum m ation of term s w ith a leading (a^ In a;)" in the expansion of E quation (2.18),

independent of In This involves considering the evolution of a gluon d istribu tion

which is not in tegrated over /c^, since breaking the association to leading In

implies th a t the gluon ladder need not be ordered in hr- T he unin tegrated gluon

density is related to the m ore fam iliar gluon d istribu tion by

2x g { x , Q ‘̂ ) = J ^ Q ( x , k T ) (2.19)

34


y,Q

Figure 2.5: Schematic representation of the gluon ladder and quark box 5 .

The BFK L equation then describes the ln (l/a :) evolution of the un in tegrated gluon

density:

dÇ{x, k f)(2 .20)

d ln { l / x )

This evolution corresponds roughly to cascades w ith emissions strongly ordered in

X w ith no restric tion on h r -

In order for the BFK L equation to make predictions, e.g. of F2 , the gluon ladder

m ust be convoluted w ith the quark box (Figure 2.5) according to th e hr factorisation

theorem :

1

F2{x ,Q^) = [ ~ [ (2 .2 1 )J y J i T̂ V

2.2.2 CCFM evolution

W hereas the conventional D G LA P equations deal w ith evolution and may

be inadequate a t low x, the BFK L equation deals w ith 1 /x evolution and may

be inadequate a t high The C iafaloni-C atani-F iorani-M archesini (CCFM ) [20]

35

C hapter 2 2.3 Photon structure

evolution equations a ttem p t to be applicable across the whole kinem atic plane by

sum m ing more general classes of diagram s. They are based on the idea of coherent

gluon rad ia tion , which leads to angular ordering of gluon emissions in the gluon

ladder such th a t 6i > 9i-\ where 6i is the ith gluon makes to the original direction.

O utside th is angular region there is destructive interference such th a t m ulti-gluon

con tribu tions vanish to leading-order. A ngular ordering implies ordering in k r / E of

the gluon ladder. Because of angular ordering, the unin tegrated gluon d istribu tion

in CC FM depends on the m axim um allowed angle, in addition to the m om entum

fraction x and the transverse m om entum of the propagator gluon. This ex tra scale

can be taken to be the scale Q of the probe, leading to a scale dependent gluon

density

At sm all T, where A becomes independent of and ordering m k T / E does no t im ply

ordering in the integral equation for A{x , k^, can be approxim ated by the B FK L equation. However, a t m oderate x, kr ordering is im plied and the D G LA P equation for the in tegrated gluon d istribu tion g[x^ Q^)is recovered. Cross sections

can then be calculated according to the kr factorisation theorem by convoluting the un in teg rated gluon density w ith the off-shell boson gluon fusion m a trix elem ent, d,

cr = y* dk^dXgA{xg, kT^Q) î'y*9* ^ (2.22)

2.3 P h oton structure

T he DIS cross section, given in E quation (2.9), is dom inated by the exchange of

very low v irtuality photons. The lifetim e of these photons varies as ^E^jQ^ which

a t very low virtualities can be long com pared to th e characteristic tim e of the hard

subprocess. The electron beam can then be considered a source of approxim ately

massless, collinear, photons and an ep collider effectively becomes a 7 p collider. The

to ta l cross section, .y(p) which is the probability of finding a

photon w ith energy E^ = yE^ inside th e electron. In the lim it -4- 0, the photons

can only be transversely polarised, and to a good approxim ation

(2.23)

where the photon flux is Q^), is given by

36

Chapter 2 2.3 Photon structure

^ 220DL98

ALLM97

PDG96180 -

140

200

100

170

200 210 220

100

Figure 2.6: The total photon-pj'oton cross section.

1 + (1 - v Y _ c ^ - y Q 2rnin (2.24)

where = rjLjy'^/{l — y) is the kiiieniatic lower bound. This is known as theequivalent photon approxim ation (EPA). Neglecting the Q' ̂ dependence of the 7 p

interaction and integrating over photon virtualities from the lower kinem atic lim it

to some m axim um , , yields

a 1 + (1 - _ 2 -̂ ~ 1 - Q2m in (2.25)

^ z/ \ Q L

which is the W eizsacker-Williams approxim ation (WWA) [21].

Figure 2.6 shows a/JJ measured a t HERA together w ith the results from low energy

experim ents [21]. The shape strongly resembles th a t of rneson-nucleon scattering

and can be described using the same models. Here, bo th photon and proton

behave as objects with spatial extent. These types of events are term ed “soft”

photoproduction. At larger m om entum transfers, high transverse m om entum je ts

of hadrons are produced, and the meson-nucleon model of scattering is no longer

able to explain the observed final state. It can however be explained in term s

of parton-parton scattering, where the partons which collide to produce je ts of

hadrons are considered to be point-like. These types of events are term ed “hard”

photoproduction and will now be discussed in more detail.

37


(a) (b) (c)

(d) _ (e) , (f)

Figure 2.7: Examples of leading-order processes resulting in two jets; (a) QCD Compton, (h) boson gluon fusion, (c) flavour excitation from the proton, (d) gluon gluon fusion, (e) and (f) ft,avour excitation from the photon.

2.3.1 Hard photoproduction

At leading-order, hard photoprodiiction processes, such as those in Figure 2.7, can

he s])lit into two classes; “d irect” , where the photon takes part directly in the hard

scatter (Figures 2.7(a)-(c)), and “resolved” , where a parton from the photon takes

part in the hard scatter (Figures 2.7(d)-(f)) and the scatter can be viewed as having

resolved the structu re of the photon.

These two classes of events can be separated based on the knowledge of the fraction

of the photon’s m om entum participating in the hard scatter, x^. For the LO QCD

diagram s shown in Figure 2.7, energy and m om entum conservation yield

E m p a r i o n s _ ^ p a r t o n 3partons T ^

“ 2yE, '

where yEf, is the initial photon energy. For direct events, this is one and for resolved

events it is less than one. By summing over je ts instead of partons can be

translated into an experim entally m easurable ciuantity, , and Equation (2.26)

becomes:

y.obs _ C ^ je ts T _________ 0 7 ^

“ 2 ,/E , ’

38


ZEUS 19942000

> 1750

1500

1250

1000

750

500

resolved direct250

Figure 2.8: The distribution in dijet events for data (black dots) compared with HERWIG with and without MPI (solid line and dotted line), and PYTHIA with MPI (dashed line) Monte Carlo generators.

where the sum runs over the two highest transverse energy je ts and is the

fraction of the pho ton ’s m om entum entering the d ijet system.

The ability to separate direct and resolved events using 2;°̂ ̂ was dem onstrated

in [22]. F igure 2.8 shows the the m easured d istribu tion together w ith the

predictions of two LO M onte C arlo’s. D irect events (filled histogram ) are strongly

peaked a t x̂ ^̂ > 0.75 and the resolved a t x°̂ ̂ < 0.75.

Beyond leading-order th e separation between direct and resolved is am biguous; the

processes in Figures 2.7(d) and (e), classed as the resolved production of two je ts a t

LO could be considered as the direct production of th ree je ts a t NLO. The term s

direct and resolved are then only defined a t leading-order, beyond th is they depend

on the factorisation scale and can thus have no physical m eaning. T he definition

of , however, is valid a t all orders and it rem ains a powerful too l to identify

“photon struc tu re like” effects.

2.3.2 Photon structure functions

The struc tu re of the photon is measured directly in deep inelastic 0 7 sca ttering [23],

shown in Figure 2.9, which is form ally analogous to deep inelastic ep scattering. The

cross section for a probing photon, virtuality, = —q ,̂ scattering off a real ta rg e t

39


%

10 10 10 10Q- ((;eV-)

Figure 2.9: Feynman diagram for ê y diagram with a virtual photon, j* , probing an on-shell photon, 7 (left). Summary of current results on jRj (right).

photon w ith virtuality^ ^ 0 producing a final s ta te e X is given by,

^ [ ( 1 + (1 - VŸ) m - , Q^) - y ^ m - , Q ')] (2 .2 8 )

As in ep scattering the s tru c tu re function can be w ritten in term s of the parton

densities

F i ( ï , = 2 ï y ] e]qj{x, Q^), (2.29)

where the sum runs over all quark flavours, i, of charge and the factor of

two accounts for quarks and anti-quarks. These p arton densities obey a set of

inhom ogeneous evolution equations [24]:

dqj{x,Q'^) . X 0 5̂(Q^) fdlogQ^ ^ ^ 2tt J y

(2.30)

d g (x ,Q ‘̂ ) as {Q ‘̂ ) f d^

ydlogQ ' 27T+ Pgg 9{y,Q^) (2.31)

'^This is the nomenclature used in two-photon interactions at LEP. Unfortunately, at HERA, denotes the virtuality of the probed photon and the scale of the probing interaction is ~ Thus, to go from LEP to HERA nomenclature, -> and Q ^ .

40

Chapter 2 2.4 Virtual photon structure

where

a{x) = 3e^— \x ̂ + (1 — x)^] . (2.32)

These are the s tandard D GLA P evolution equations, e.g. for th e pro ton , except for

the so-called anom alous term , a(x), which comes from branchings 7 —)■ qq, and is

unique to the photon evolution equations. The solution can be w ritten as th e sum

of two term s [25],

Q') = Q'; QD + Q'; Q l ) (2.33)

where a = fqi{x,Q^) = qi{x,Q‘̂) and /g (x ,Q ^) = g{x,Q^). T he first term is a solution to the homogeneous equation w ith a non-pertu rbative inpu t at Q = Qo, and the second is a solution to the full inhom ogeneous equation w ith the boundary

condition f]'^'^{x,Ql-,Ql) = 0. One possible physics in terp re ta tion is to let

correspond to 7 -4- V fluctuations, where V = J /^ ; , . . . is a set of vector

mesons, ( “vector meson dom inance” ), and let correspond to pertu rba tive

J ^ qq fluctuations, q = u , d , s , c and b ( “anom alous” ). T he discrete spectrum

of vector mesons can be combined w ith the continuous (in v irtua lity spectrum

of qq fluctuations to give

2

/2(^,Q ") = E Q ' ; Q o ) + ^ E 24 [ ^ / a ' ” (x ,Q ';k^) (2.34)y I v i-K ̂ J kVo

where each com ponent, and obeys a un it m om entum sum rule.

There are currently a large num ber of photon p arton density param eterisa tions

and usually involve some fits to data . W ith the large errors on additional

assum ptions need to be made. These assum ptions differ in different m odels and

involve the trea tm en t of heavy quarks, the choice of the scale Q l and the m ethods

of deciding the form of the inpu t densities.

2.4 V irtual p hoton structure

The evolution equations (in Q^) of the PD F s of the v irtual photon can be exactly

calculated in pertu rba tive QCD for th e restric ted range Q l Q^.

41

Chapter 2 2.4 Virtual photon structure

d^O / dx°®® d o ' d f g p ' fp jb /G e V ^ ;(E j)^ G tV ')= 49-85 ^ 85-150

•ZEUS 96/97 y’p— SaS ID (HERWIG 5.9)— GRV LO (HERWIG 5.9)

5

§?

§

• 96/97 ZEUS Preliminary

Figure 2.10: Triple differential cross section d^a/dx^^^dQ^dEj^ as a function of

for different regions in and E^(left). The ratio of cross sections R = < 0.75)/cr(T°^ > 0.75) as a function of (right).

Theoretically challenging, however, is the region ^ ^ Q o where evolution

equations cannot be derived from pertu rba tive QCD.

In [26] PD Fs th a t are valid for all 0 < were proposed and a generalised

form of Equation (2.34) given:

+

V

a em27T Y.Hj

dE“p2 VA;2 + p 2 (2.35)

Ql

T his extension of real-photon P D Fs to those of the v irtual photon can be applied

to any set of parton d istribu tions, provided th a t the VMD and anom alous p arts are

available separately.

2.4.1 Experimental review

M easurem ents of the v irtua l photon struc tu re in tw o-photon in teractions require

the detection of bo th scattered leptons a t non-zero scattering angles. This was first

done by the PLU TO collaboration in 1984 [27] and, more recently, by L3 [28] and

OPAL [29]. However, all these analyses suffer from low statistics. T he extensive

42

Chapter 2 2.5 Heavy flavour production

range, together w ith the large centre-of-mass energies, available a t HERA enable

m ore detailed studies of the evolution of photon struc tu re [30-32].

Two recent results from ZEUS are shown in Figure 2 .1 0 . T he m easured trip le

differential dijet cross sections (Pa/dx^^^dQ‘̂ dE^ are shown as a function of in

different bins of and E^. For each bin, the cross section in the low region

falls faster w ith increasing th a n the cross section in the high region. For

the bins w ith > Ej, the d a ta are well described by the HERW IG predictions

including only LO direct processes. In the bins w ith < E^ LO direct processes

alone are not enough to describe the data.

The faster fall of the low region can be seen more clearly in the ra tio of

cross sections R = < 0. 75) / a > 0.75). The ra tio of the d a ta falls

w ith increasing Q'̂ . The HERW IG prediction, using the suppressed v irtual photon

s truc tu re function SaSlD [25], also falls w ith increasing and describes the shape

b u t no t the norm alisation of the ra tio (requiring a norm alisation factor of 1.3).

2.5 H eavy flavour production

The conventional QCD parton m odel is form ulated in the zero m ass parton lim it.

T here are two basic m ethods of trea tin g charm in the evolution equations based on

the factorisation equation [33]

a^ ^ x{S ,Q ^ ) = Y^qi{x, i i^) (2.36)i

where i is the sum over all flavours which can actively partic ipa te in the in teraction

a t th e energy scale Q^. â is the cross section for th e hard scatter which

is convoluted w ith the parton d istribu tion functions qi{x,fi^) where fi is the

factorisation scale. C harm can then either be included in the sum as an active

flavour above some threshold (variable flavour num ber (YEN)) or excluded from

the in itia l s ta te and trea ted separately (fixed flavour num ber (F F N )). In principal,

the two alternatives can be regarded as two different bu t equivalent schemes for

organising the pertu rba tion series in pQCD. In practice, since the p e rtu rb a tio n series

is te rm inated after one or two term s, the effectiveness of the two approaches can be

quite different in different kinem atic regions. For a full review of the theoretical and

experim ental s ta tu s of heavy flavour production see, for exam ple, [34] and references

therein.

43


M a ss iv e F F N 3 sc h e m e

In th is scheme, the num ber of active quark flavours is fixed, independent of Q^. Only

light quarks (u, d, s) are included in the in itia l s ta te pro ton and photon and charm

quarks are only produced dynam ically in the hard process. T he presence of th e two

large scales^, (j? and m^, can spoil the convergence of the pertu rba tive series because

the neglected term s of orders higher than contain log(//^/m ^) factors th a t can

become large. Therefore the results of massive FFN 3 calculations are expected to

be m ost accurate a t /i^ ~ and to become less reliable when ^ m^.

M a ss le s s V F N sc h e m e

In this scheme, charm is trea ted as an additional active flavour w ith zero mass above

some threshold, ~ In th is way, the large logarithm s in present a t high

fl are au tom atically resum m ed. This m eans th a t besides charm produced in the

hard process flavour excitation processes are also included. Therefore the results of

massless V FN calculations are expected to be m ost accurate a t ^ m l and to

become less reliable when

2.5.1 Experimental review

D e e p in e la s t ic s c a t te r in g

Early studies of charm production in DIS [35] suggested th a t the p roduction of

charm ed mesons in ep collisions is dom inated by the boson gluon fusion (BG F)

mechanism, already shown in Figure 2.7(c). C alculations for th is process exist to

NLO and the cross section depends directly on th e gluon density in the proton. If

the gluon density from the inclusive m easurem ent of F2 are used in the calculation,

the results can be com pared to the m easured charm cross section, giving a powerful

cross check of pQ CD which states th a t the same, universal, gluon d istribu tion should

contribute to bo th the inclusive structu re function F 2 , and the exclusive charm

struc tu re function In addition, the presence of two large scales, namely, the

v irtuality of the exchanged boson {Q^) and the square of the charm quark mass

{ml), provides a testing ground for resum m ation techniques. F igure 2 .1 1 show the

differential D* cross sections m easured a t ZEUS com pared to a massive FFN 3 NLO

calculation [36] which uses the gluon density ex tracted from fits to F2 as input.

The description of the Q^, x and W d istribu tions is very good, confirm ing the

^In DIS fjL is the photon virtuality, Q , in photoproduction it is p r -

44


ZEUS 1996-97

SJ) 1b

ZE U S 1 9 9 6 - 9 7

log,„x

P t ( D ') (GeV) 77(D-)

W(GeV)

I , = 0.00005(x 4*)

. i- 0.00013(x 4’)

J 0.00030(x 4')

0.00050(x 4‘)

0.00080(x 4*)

0 .00120(x 4’)

r^ '0.00200(x4")

^ 0.00400(x 4')

0 .00800(x4’)

^ ZEUS NLO QCD0.02000(x4°)

(GeV̂)Figure 2.11: Differential cross sections for D* production in DIS. The open (shaded) band shows the result of an NLO QCD calculation using Peterson (R A P G A P extracted) fragmentation (left). as a function of x and (right).

universality of the gluon d istribu tion . However, in order to describe the p t {D *) and

t]{D*) d istribu tions it was necessary to use a charm fragm entation ex tracted from

the LO M onte Carlo R A PG A P. W ith th is fragm entation included the description

is good enough to be used to ex trapo la te the m easurem ent into the full D* phase

space and ex tract The m easured Fff ̂ is com pared to the value derived from the

gluon d istribu tion extracted from NLO fits to F2 in Figure 2 .1 1 .

Photoproduction

NLO calculations for the pho toproduction of heavy quarks such as charm also exist,

where the heavy quark m ass or the high transverse m om entum of the produced

partons is used as the hard scale. Significant differences between calculation

schemes can be expected since massless V FN calculations will include charm

excitation processes and thus predict, for a given factorisation scale, a larger

resolved com ponent in com parison w ith a massive FFN 3 calculation. Therefore, it

is interesting to com pare the predictions of these models to d a ta and to investigate

th e sensitivity of the experim ental results to the partonic content of the photon and

specifically to the charm excitation contribution.

Figure 2.12 shows the differential cross section da/dp^* for various ranges of pt

m easured a t ZEUS com pared to bo th massive and massless calculations [37]. As

expected as p r —̂ me the description of the d a ta by th e massless calculation

degrades. However, the NLO predictions generally lie below the d a ta , particu larly

45


Z E U S 1 9 9 6 + 9 7 ZEUS 1996+97(a)p^D ->2G eV

V • D -» {K n) \ Massive, e *

Massive, )ip = 0.5 m ., aa

I 10

n

(b) p^D- > 3 GeV

(upper)

S 5

— Herwig: direct + resolved r/XJ Herwig: direct

Herwig: resolved Herwig: resolved without

(d) Pĵ D- > 6 GeV(c) Pĵ D- > 4 GeV • D -> (K n) ÏI, D D -» (Kirmi); f

QT

■D

(b)

Massive NLO, parlon level, e- 0.02

— p„ = 1.0 m , riij = 1.5 GeV

- -- = 0.5 m^, = 1.2 GeV

Figure 2.12: The differential cross section da/drj^* for photoproduction compared to several NLO calculations (left). The differential cross section da/dxf^^ for dijets with an associated D* (right) compared to LO (upper) and NLO (lower) predictions.

in the forward region, in all the plots. Given the discrepancy between d a ta and

NLO predictions in the inclusive D* m easurem ents it is im po rtan t to study the

kinem atics of charm production in more detail. This was done in the sam e paper by

m easuring the dijet cross section as a function of , also shown in Figure 2.12.

A t LO the d a ta require a resolved contribution of 45%, th is com pares to 75% for

th e cross section of Figure 2.8 which did not require the presence of a D*. The

charm excitation contribution to the LO resolved process was 93% in the M onte

Carlo. The prediction of a massive NLO calculation, lies significantly below the

d a ta for < 0.75, however a massless calculation could be expected to give a

b e tte r description.

46

Chapter 3

K inem atic reconstruction

T he event and je t kinem atics m ust be reconstructed from m easured quantities. The

m ethods used for the reconstruction of the event variables in th is thesis are now

described.

3 .1 R e c o n s t r u c t io n o f y a n d

T here are m any ways of reconstructing the variables y and [38], two of which are

used in th is thesis; the “electron” and “Jacquet-B londel” m ethods.

3.1.1 Electron m ethod

T h e electron m ethod is theoretically simple and relies only on the knowledge of

th e energy of the scattered lepton, E' ̂ and the angle of the scatter, 6e- For a given

in itia l lepton energy, Eg, th e variables, y and can be calculated from the scattered

le p to n ’s energy E' ̂ and polar angle 6e as follows;

He = ̂ (1 — cosOe) , (3.1)

+ (3.2)

T h is assumes th a t there were no additional emissions from the lepton, i.e. th a t it

en tered the hard scatter w ith the beam energy Eg and it left w ith the m easured

energy E ' and as a result is sensitive to bo th initial- and final-state electroweak

rad ia tiv e corrections (ISR and FSR).

47

Chapter 3 3.2 Jet reconstruction

3.1.2 Jacquet-Blondel method

T he Jacquet-B londel m ethod [39] calculates the variables y and from the hadronic final s ta te and can thus be used when the scattered lepton is not measured. The hadronic final s ta te is defined as all particles except th e scattered lepton and sum m ing over these gives:

(3.3)

+ (3.4)1 - yjB

E xperim entally this sum is not over hadrons b u t calorim eter cells. If the scattered lepton is found in the calorim eter, then the cluster of cells associated w ith it are elim inated from the calculation. If the scattered lepton is m isidentified its energy deposit will enter into the above sum m ations. This results in high values of ?/jb , allowing events w ith an unidentified electron to be rejected.

Since th is m ethod measures the energy transferred to the hadronic system , it is unaffected by FSR, however it will still be sensitive to ISR th rough Eg.

R esolutions

T he resolutions on y and using the two m ethods described above are shown in F igure 3.1. The resolution is significantly worse using th e Jacquet Blondel m ethod. This is a result of energy lost due to dead m ateria l and acceptance. As a result, Q jg is only used in high-Q^ events when there is no scattered electron, i.e. charged current DIS. Thus, when an electron is present in an event the electron m ethod has been used to reconstruct Q^. W hen there is no identified lepton, is restric ted to be below 1 GeV^ by means of an an ti-tag requirem ent (see Section

4.3).

T he y resolution is again b e tte r using the electron m ethod, and there is a system atic bias in the m easurem ent of yjB due to energy loss in dead m ateria l before the GAL. However, in order to be consistent a t different regions, yjB is used for the estim ate of y w hether or not an electron is found.

3.2 Jet reconstruction

There are two types of je t algorithm in com m on use; the “cone” and “cluster” algorithm s. In the analysis presented in th is thesis bo th types of algorithm are

48


1400800700600500400300200100

1200

1000

800

600

400

200

- 0.3 - 0.25 0.250.3 0

20001750150012501000750500250

100045040035030025020015010050

800

600

400

200

1 1 - 0.4 0 0.4 - 0.4 0.40

Figure 3.1: y and resolutions using the electron and Jacquet Blondel methods.

used. The EU CELL cone algorithm is used in the online trigger selection, described

in Section 4.2, and the KTCLUS [40] algorithm is used in the offline selection,

described in Section 4.3, and the cross section definition of Section 4.1.

D etailed discussions of each of these can be found elsewhere [41], so only a brief

description is included here.

3.2.1 Cone algorithm

The Snowmass Convention [42] for cone algorithm s defines th e transverse energy

and the coordinates of a cone je t as;

i

(3,5)

T i

49


where the sum runs over all hadron or calorim eter cells w ith in the cone defined by

a given prescribed radius, i?, in 77 — ^ space.

In EUCELL, the hadrons/cells are clustered using a grid in 77 — ^ space. The size of the cell

Documents

Charm and the Virtual Photon at HERA and a Global Tracking ...€¦ · Charm and the Virtual Photon at HERA and a Global Tracking Trigger for ZEUS Benjamin John West UCL University