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

  • Introduction

  • BFKL PomeronCalculus and RFT

  • Semiclassicalapproximation

  • Solutioninsidethesaturationregion

  • Application and Conclusion


  • High EnergyScattering

  • DifractiveScattering and DIS



  • h-h h-NucleusCollision:

    dilute/dilute - dense sistema

  • Nucleus - NucleusCollision

    Dense-Dense systems

Scattering approach

  • 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


  • Theamplitude can be described

    considering a Pomeron Green Function BFKL propagator

    SeeLipatov “ Perturbative QCD”

  • Where

    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


    forsmallkt and largesize of gluon and strongyoverlap

    fusiongg –> g are important


Experimental evidence in small x
Experimental evidence in small-x


First: Modification of the BFKL

1983 GLR Gribov, Levin and Ryskin

1999 BK Balisky- Kovchegov:


BK eq. evolution for Amplitude N(r,b,Y)

See hep ph 0110325
See 0110325

  • BK equation DIS virtual photon on a large nucleus


  • 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

Approchtosaturation II

Color GlassCondensate CGC

Clasiccalfieldfor QCD withWeizsacker-Williams generalized Field

Muller and Venogapalan


J. Jalilian-Marian, E. Iancu, Mc Lerran, H. Weiger, A. Leonidovt and A. Kovner

RenormalizationGroupApproach in the Y-variable

Generalization to pomerones interaction

  • 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



Equations and definitions
Equations and definitions


  • BFKL if

  • BK

Semiclasical approach

Numerical solution

  • Expandingaround


  • Physical Condition to select solution

  • Extension to Y dependence

  • AplicationtoScatteringdilute-Dense


  • 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