Quark pair production using dipole formalism in neutrino-proton scattering

at high energies *

Mairon Melo Machado

High Energy Phenomenology Group, GFPAE IF – UFRGS, Porto Alegre

melo.machado@ufrgs.br

www.if.ufrgs.br/gfpae

* In collaboration with M. B. Gay Ducati and M. V. T. Machado

Outline• Lepton-nucleon collision

• Color dipole formalism

• Structure functions

• Neutral Current (NC) process

• Neutrino-nucleon cross section

• Results and conclusions

Motivations

• Interaction of high energy neutrinos on hadron targets are an important probe to test QCD and to understand the parton properties of hadron structure

• Combinations of neutrino and anti-neutrino scattering data used to determine the structure functions

• The structure function F2 is the singlet distribution

• Phenomenology using saturation models within the Color Dipole Approach successfully describes current small-x data 1

• Purpose of a new high-energy, ultra-high statistics neutrino scattering experiment (NuSOnG)

1GAY DUCATI, M. B., MACHADO, M. M., MACHADO, M. V. T.

– PLB 644 (2007) 340;

Neutrino-nucleon collision

M is the nucleon mass

E is the neutrino energy

p and q are the nucleon and boson four-momenta

Z (q)

pi

p’j

pj

pk

GF is the Fermi constant

1.166.10-5 GeV-2

Mi is the boson mass

F2, FL and F3 are the structure functions

Neutrino-nucleon cross section

)()1)(( 22)(

xqxyxxqEmG

dxdy

d NFN

22)(

)1)(()( yxqxxxqEmG

dxdy

d NFN

2 ROBERTS, R. G., “The structure of the proton”, Cambridge University Press (1993);

2

Color dipole phenomenology ’s are the wave functions for electroweak bosons

z is the momentum fraction of quark and (1-z) is the momentum fraction of the antiquark

1 and 2 are the helicities of the quarks (1/2 or -1/2)

r is the transversal size of the dipole

dip is parametrized and fitted to the experiment .

Structure functions

Chiral

coupling

sin 2 θW = 0.23120

K0,1 are the McDonald functions

Quark distribution

• Gluon emits a quark-antiquark pair changing the quark distribution in the nucleon

• These quarks are called sea quarks

• Quark content is given by the sum of valence quarks and sea quarks

Dipole cross section

• Golec-Biernat-Wusthoff (GBW) 3

• Iancu-Itakura-Munier (IIM) 4

, 0 = 23 mb, ~ 0.288, x0 ~ 3.10-4 m, mf = 0.14 GeV

4exp1),(

22

02 sat

dip

Qrrx

HEP 08

Y=ln(1/x), BCGC = 5.5 GeV-2

3 GOLEC-BIERNAT, K; WUSTHOFF, M. PRD 60, 1140231 (1998);

4 IANCU, ITAKURA, MUNIER, PLB 590, 199 (2004);

Neutrino-nuclei interaction 5

Dipole cross section for bosons transversally or longitudinally polarized are extended for nuclei using Glauber-Gribov formalism

Nuclear profile function TA (b)

b is the impact parameter and n(r) is the nuclear matter density normalized as

HEP 08

|),(|),( 2, rxQx ARL

21

21

,.

22,,

1

0

2 ),(),,(

rxQrzdzrd AdipRL

)()( 22 bzdznbTA

Arrnd )(3

5 WATT, G. KOWALSKI, H. PRD 78 (2008) 014016

Structure functions (x fixed)

Virtuality dependence for b-CGC and GBW models

Small deviation more sizable at large Q2

Quarks (d,s) dominat over u

Electroweak couplings

Charm contribution 13%

Structure functions (Q2 fixed b-CGC model)

Dependence approximatelly power-like with an effective power which growths on Q2

λ(Q2=1 GeV2) ~ 0.12

λ(Q2=M2Z) ~ 0.224

Unusual behavior in the limit of large Q2 and large x

Structure functions (Q2 fixed GBW model) Estimates the uncertainty from the theoretical side

GBW model does not include the QCD evolution in the dipole cross sectin

Effective power is similar to the b-CGC model

FL being distinct at Q2=M2Z

Flattening in FL is stronger in b-CGC than in GBW

NC charm structure functions

Q2 xF2

F3

F2

F3

Neutral Current Cross Section Results

Energy (GeV) σcharm (cm2) σCharm/ σTotal

27 5,4 x 10-40 0,027

154 1,9 x 10-38 0,135

1000 7,1 x 10-37 0,154

10000 3,0 x 10-35 0,193

100000 3,3 x 10-34 0,225

Contribution of sea quarks dominates at high energies

neutrino-proton interaction

6 KWIECINSKI, J. et al. PRD 59 (1999) 093002

6

Neutral Current Cross Section Results

Energy (GeV) σcharm (cm2) σCharm/ σTotal

27 6,56 x 10-44 3,25 x 10-3

154 2,33 x 10-42 1,04 x 10-2

108 5,8 x 10-33 0,25

109 1,4 x 10-33 0.41

neutrino-nuclei interaction

0.23 fb

Analysis of small-x neutral current neutrino-nucleus is performed within the color dipole formalism

Structure functions F2 and FL are investigated

Employement of two phenomenological parametrizations for the dipole cross sections which succesfully describe small-x data

Deviations among the models at very small-x data

Further investigations are requested

Computation of the charm content to the total NC neutrino cross section consistent with current experimental measurements

Conclusions