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Nonlinear evolution for Pomeron fields in the semi classical

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### 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

Outlook

- Introduction
- BFKL PomeronCalculus and RFT
- Semiclassicalapproximation
- Solutioninsidethesaturationregion
- Application and Conclusion

Introduction

- High EnergyScattering
- DifractiveScattering and DIS

:

Pomeronexchange

- h-h h-NucleusCollision:

dilute/dilute - dense sistema

- Nucleus - NucleusCollision

Dense-Dense systems

Scatteringapproach

- d=2 tranversespace
- saturación regionQs >>

C are

smallthenwe can considerthat

semiclasicasapproach are valid

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”

Dipole the wave function hep-th/0110325

- Approximation r, R << b then it is independent of b impact parameter

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

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)

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

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

GeneralizationtoPomeronesInteraction

- 1P 2P
- 2P 1P
- Loop de Pomerones

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

QCD results and effectiveaction

- Green Function
- Definition of a Field Theory RFT

See M. Braun or E. Levin

target / projectile

Solutions:

momentumrepresentation

- Solution: Characteristicamethod

Using the relation BFKL Pomeron

L. Gribov, E. Levin and G. RyskinPhy. Rep. 100 `83

- One can show that
- And that

- And we use de condition

NumericalSolution

- Expandingaround

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

Kinematic Variables

- Q resolutionPower
- X measure of momentumfraction of struck quark
- F(x,Q)

General Behaviour

- Bjorken Limites DGLAP
- Regge Limite

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