Nonlinear evolution for pomeron fields in the semi classical
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Nonlinear evolution for Pomeron fields in the semi classical. C. Contreras , E. Levin J. Miller* and R. Meneses Departamento de Física - Matemática Universidad Técnica Federico Santa María Valparaiso Chile *Lisboa Portugal SILAFAE 2012 Sao Paulo Brasil. O utlook.

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Nonlinear evolution for pomeron fields in the semi classical

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


O utlook
Outlook

  • Introduction

  • BFKL PomeronCalculus and RFT

  • Semiclassicalapproximation

  • Solutioninsidethesaturationregion

  • Application and Conclusion


Introduction
Introduction

  • High EnergyScattering

  • DifractiveScattering and DIS

    :

    Pomeronexchange

  • h-h h-NucleusCollision:

    dilute/dilute - dense sistema

  • Nucleus - NucleusCollision

    Dense-Dense systems


Scattering approach
Scatteringapproach

  • d=2 tranversespace

  • saturación regionQs >>

    C are

    smallthenwe can considerthat

    semiclasicasapproach are valid


Description in qcd
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”


Nonlinear evolution for pomeron fields in the semi classical

  • Where

    Dipole the wave function hep-th/0110325

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


Nonlinear evolution for pomeron fields in the semi classical

  • 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


Experimental evidence in small x
Experimental evidence in small-x


Nonlinear evolution for pomeron fields in the semi classical

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)


See hep ph 0110325
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


Nonlinear evolution for pomeron fields in the semi classical

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


Generalization to pomerones interaction
GeneralizationtoPomeronesInteraction

  • 1P  2P

  • 2P 1P

  • Loop de Pomerones


Pomeron loops see e levin j miller and a prygarin arxiv 07062944
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 effective action
QCD results and effectiveaction

  • Green Function

  • Definition of a Field Theory RFT

    See M. Braun or E. Levin


Funcional integral braun 00 06
Funcional Integral Braun ´00-06


Nonlinear evolution for pomeron fields in the semi classical


Solutions
Solutions:

momentumrepresentation


Equations and definitions
Equations and definitions

Thisequationisequivalentto:

  • BFKL if

  • BK


Semiclasical approach
SemiclasicalApproach


Nonlinear evolution for pomeron fields in the semi classical


Nonlinear evolution for pomeron fields in the semi classical


Nonlinear evolution for pomeron fields in the semi classical



Numerical solution
NumericalSolution

  • Expandingaround


Conclusion
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
Kinematic Variables

  • Q  resolutionPower

  • X  measure of momentumfraction of struck quark

  • F(x,Q)


General behaviour
General Behaviour

  • Bjorken Limites DGLAP

  • Regge Limite