1. High Energy Phenomenology Group, GFPAE IF – UFRGS, Porto Alegre
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
* In collaboration with M. B. Gay Ducati and M. V. T. Machado
Mairon Machado

2. Outline Lepton-nucleon collision Color dipole formalism
Structure functions
Neutral Current (NC) process
Neutrino-nucleon cross section
Results and conclusions
Mairon Machado

3. 1GAY DUCATI, M. B., MACHADO, M. M., MACHADO, M. V. T.
– PLB 644 (2007) 340;
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)
Mairon Machado

4. Neutrino-nucleon collision
Z (q)
p’j pi
M is the nucleon mass
E is the neutrino energy
p and q are the nucleon and boson four-momenta pj pk
Mairon Machado

5. Neutrino-nucleon cross section2
GF is the Fermi constant
GeV-2
Mi is the boson mass
F2, FL and F3 are the structure functions
2 ROBERTS, R. G., “The structure of the proton”, Cambridge University Press (1993);
Mairon Machado

6. 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 .

7. Structure functions sin 2 θW = 0.23120 Chiral coupling
K0,1 are the McDonald functions
Mairon Machado

8. 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
Mairon Machado

9. Dipole cross section Golec-Biernat-Wusthoff (GBW) 3
3 GOLEC-BIERNAT, K; WUSTHOFF, M. PRD 60, (1998);
4 IANCU, ITAKURA, MUNIER,
PLB 590, 199 (2004);
Golec-Biernat-Wusthoff (GBW) 3
Iancu-Itakura-Munier (IIM) 4
, 0 = 23 mb,  ~ 0.288, x0 ~ m, mf = 0.14 GeV
Y=ln(1/x), BCGC = 5.5 GeV-2
HEP 08

10. 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
5 WATT, G. KOWALSKI, H. PRD 78 (2008)
HEP 08

11. 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 %
Mairon Machado

12. 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
Mairon Machado

13. 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
Mairon Machado

14. NC charm structure functionsQ2 x F2 F3 F3
Mairon Machado

15. Neutral Current Cross Section Results6
neutrino-proton interaction
Contribution of sea quarks dominates at high energies
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
6 KWIECINSKI, J. et al. PRD 59 (1999)
Mairon Machado

16. Neutral Current Cross Section Results
neutrino-nuclei interaction
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
0.23 fb
Mairon Machado

17. Conclusions
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
Mairon Machado