Nonlinear evolution for pomeron fields in the semi classical
Download
1 / 35

Nonlinear evolution for Pomeron fields in the semi classical - PowerPoint PPT Presentation


  • 52 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Nonlinear evolution for Pomeron fields in the semi classical' - olathe


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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”


  • 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

    but

    forsmallkt and largesize of gluon and strongyoverlap

    fusiongg –> g are important

    Saturationphenomena


Experimental evidence in small x
Experimental evidence in small-x


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


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



Solutions
Solutions:

momentumrepresentation


Equations and definitions
Equations and definitions

Thisequationisequivalentto:

  • BFKL if

  • BK


Semiclasical approach
SemiclasicalApproach






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


ad