Nonlinear evolution for Pomeron fields in the semi classical

1. Nonlinear evolution for Pomeronfields in the semi classical C. Contreras , E. Levin J. Miller* and R. MenesesDepartamento de Física - Matemática Universidad Técnica Federico Santa María Valparaiso Chile *Lisboa Portugal SILAFAE 2012 Sao Paulo Brasil

2. Outlook • Introduction • BFKL PomeronCalculus and RFT • Semiclassicalapproximation • Solutioninsidethesaturationregion • Application and Conclusion

3. Introduction • High EnergyScattering • DifractiveScattering and DIS : Pomeronexchange • h-h h-NucleusCollision: dilute/dilute - dense sistema • Nucleus - NucleusCollision Dense-Dense systems

4. Scatteringapproach • d=2 tranversespace • saturación regionQs >> C are smallthenwe can considerthat semiclasicasapproach are valid

5. Description in QCD • The interactionbetweenparticlesisviainterchange of Gluons: Color Singlet BFKL Pomeron Balinsky-Fadin-Kuraev-Lipatov • Theamplitude can be described considering a Pomeron Green Function BFKL propagator SeeLipatov “ Perturbative QCD”

6. Where Dipole the wave function hep-th/0110325 • Approximation r, R << b then it is independent of b impact parameter

7. Balitsky-Fadin-Kuraev-Lipatov BFKL equation describe scattering amplitud in High Energyusing a resumation LLA in pQCD (76-78) • BFKL evolutionequationwithrespecttoln x , which are representedby a set of Gluon ladders • Intuitive Physical Picture: BFKL difussion in the IR region: gluon radiation g -> gg in thetransversemomentumktexistlargenumber of gluons but forsmallkt and largesize of gluon and strongyoverlap fusiongg –> g are important Saturationphenomena

8. Experimental evidence in small-x

14. Approchtosaturation First: Modification of the BFKL 1983 GLR Gribov, Levin and Ryskin 1999 BK Balisky- Kovchegov: includequadratictermsdeterminedbythreePomeronVertex BK eq. evolution for Amplitude N(r,b,Y)

15. See hep.ph 0110325 • BK equation DIS virtual photon on a large nucleus LLA • Dipole approximation: photon splits in long before the interaction with nucleus degrees of freedoms • The dipole interacts independently with nucleons in the nucleus via two-gluon exchange

17. Approchtosaturation II Color GlassCondensate CGC Clasiccalfieldfor QCD withWeizsacker-Williams generalized Field Muller and Venogapalan JIMWLK / KLWMIJ Equation J. Jalilian-Marian, E. Iancu, Mc Lerran, H. Weiger, A. Leonidovt and A. Kovner RenormalizationGroupApproach in the Y-variable

18. GeneralizationtoPomeronesInteraction • 1P  2P • 2P 1P • Loop de Pomerones

19. Pomeron Loops: See E. Levin, J. Miller and A PrygarinarXiv 07062944 For example: See Quantum Chromodynamic at High Eneregy Y. Kovchegov and E. Levin Cambridg 2011 • BK resums the fan diagrams with the BFKL ladders Pomeron splitting into two ladders (GLR-DLA) • Loops of Pomeron are suppresed by power of A atomic number of the nucleus A

20. QCD results and effectiveaction • Green Function • Definition of a Field Theory RFT See M. Braun or E. Levin

21. Funcional Integral Braun ´00-06

22. Interaction with nucleus target / projectile

23. Solutions: momentumrepresentation

24. Equations and definitions Thisequationisequivalentto: • BFKL if • BK

25. SemiclasicalApproach

26. equations • Solution: Characteristicamethod

27. Using the relation BFKL Pomeron L. Gribov, E. Levin and G. RyskinPhy. Rep. 100 `83 • One can show that • And that

28. We introduce • And we use de condition

30. Solution

31. NumericalSolution • Expandingaround

32. Conclusion • Physical Condition to select solution • Extension to Y dependence • AplicationtoScatteringdilute-Dense Nucleus • Applications: Scattering amplitude • In a more refined analysis the b dependence should be taken into account • Running coupling effects sensitivity to IR region and landau Pole! • Solution in another regions

33. Preliminary Result

34. Kinematic Variables • Q  resolutionPower • X  measure of momentumfraction of struck quark • F(x,Q)

35. General Behaviour • Bjorken Limites DGLAP • Regge Limite