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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”

slide6

Where

Dipole the wave function hep-th/0110325

  • Approximation r, R << b then it is independent of b impact parameter
slide7

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

slide14

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
slide17

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

slide22

Interaction with nucleus

target / projectile

solutions
Solutions:

momentumrepresentation

equations and definitions
Equations and definitions

Thisequationisequivalentto:

  • BFKL if
  • BK
slide26

equations

  • Solution: Characteristicamethod
slide27

Using the relation BFKL Pomeron

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

  • One can show that
  • And that
slide28

We introduce

  • And we use de condition
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
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