Charm production in neutrino-nuclei collisions within the color dipole formalism at very high energies * Mairon Melo Machado High Energy Phenomenology.

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

[email protected]

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

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• 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

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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

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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

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)()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 .

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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)

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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

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|),(|),( 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(

),(

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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

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NC structure functions (Q2 fixed)

F2

FL

F3

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NC structure functions (x fixed)

F2

FL

F3

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NC charm structure functions

Q2 x

F2

F3

F2

F3

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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

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