Charm production in neutrino-nuclei collisions within the color

dipole formalism at very 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

• Lepton-nucleon collision

• Neutrino-nucleon cross section

• Structure functions

• Color dipole formalism

• Charged Current (CC) process and Neutral Current (NC) process

• Neutrino-nuclei Interaction

• Results

• Conclusions

Outline

HEP 08

• Color dipole approach (CDA) for lepton-hadron DIS

• Phenomenology using saturation models in CDA (GBW and IIM models)

• Neutrino DIS at small-x within the dipole formalism

• Analysis of charm production cross section in NC interactions

• Color dipole formalism arises as a robust theoretical approach to describe small-x structure functions1

Motivations

1 GAY DUCATI, M. B., M. M. M., MACHADO, M. V. T. – PLB 644 (2007) 340 HEP 08

Neutrino-nucleon collision

M is the nucleon mass

E is the neutrino energy

p and q are the nucleon and boson four-momenta

HEP 08

W, Z (q)

pi

p’j

pj

pk

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

HEP 08

Neutrino-nucleon cross section

GF is the Fermi constant

1.166.10-5 GeV-2

Mi is the boson mass

F2, FL and F3 are the structure functions

HEP 08

)()1)(( 22)(

xqxyxxqEmG

dxdy

d NFN

22)(

)1)(()( yxqxxxqEmG

dxdy

d NFN

Structure functions

Chiral

coupling

sin 2 θW = 0.23120

θW is the Weinberg angle

2

3

2 ROBERTS, R. G., “The structure of the proton”, Cambridge University Press 1993 HEP 08

Color dipole phenomenology

are the wave functions of quarks

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

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

r is the transversal size of the dipole

dip is parametrized and fitted to the experiment .

HEP 08

Structure functions

Structure function for bosons transversally or longitudinally polarized

K0,1 are the McDonald functions

mq (mq) is the mass of the quarks (antiquarks)

HEP 08

Neutrino-nuclei interaction

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

Dipole cross section

• Golec-Biernat-Wusthoff (GBW) 3

• Iancu-Itakura-Munier (IIM) 4

• Parameters fitted by data comparison, s = 0.63 anomalous dimension, a and b are constants

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

4exp1),(

22

02 sat

dip

Qrrx

)2(,(2lnexp1 satsat rQbrQa

)2(,2

2

0

satsat rQ

rQN

0),( rxdip

Yk

rQrx sat

sat )/2ln(

),(

HEP 08

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

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

Comparison IIM and GBW

• Total = valence + sea

Gay Ducati, MMM, Magno Machado, PLB 644 (2007) 340

HEP 08

NC structure functions (Q2 fixed)

F2

FL

F3

HEP 08

NC structure functions (x fixed)

F2

FL

F3

HEP 08

NC charm structure functions

Q2 x

F2

F3

F2

F3

HEP 08

Neutral Current Cross Section Results

High energies

contribution of sea quarks dominates

neutrino-proton interaction

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

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

5

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 1,04x10-2

108 5,8 x 10-33 0,25

109 1,4 x 10-33 0.41

1010 3,21 x 10-31 0,42

neutrino-nuclei interaction

0,23 fb

Conclusions

Description of small-x structure functions in neutrino-hadron and neutrino-nuclei interaction using color dipole formalism

GBW parametrization gives good result to proton structure functions

Extension to neutrino-nuclei interaction is suitable

Estimations gives good results in comparison to neutrino-nuclei (NuTeV and CHORUS) data for charm quark contribution

Important framework to perform estimations for future neutrino-nuclei experiments (MINERvA and Neutrino Factory)

Color dipole formalism is a good model do describes deep inelastic scattering

HEP 08