First correction to JIMWLK evolution from the classical EOMs

N. Armesto

19th International Conferenceon Ultra-Relativistic Nucleus-Nucleus Collisions (QM2006)

Shanghai, November 15th 2006

Néstor ArmestoDepartamento de Física de Partículas and IGFAE,

Universidade de Santiago de Compostelawith

Javier L. Albacete (Ohio State)and

José Guilherme Milhano (IST Lisbon)

Preprint hep-ph/0608095 (to appear in JHEP)

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Contents:

N. Armesto

First correction to JIMWLK evolution from the classical EOMs

1. Introduction.

2. The wave function formalism and JIMWLK.

3. First correction from the EOMs.

4. Relevance for phenomenology?

5. Summary.

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1. Introduction: hdQCDIancu, Venugopalan in QGP3, hep-ph/0303204

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First correction to JIMWLK evolution from the classical EOMs 3

● QCD at high densities (energies ornuclear sizes): domain of large gluondensities, recombination at work -->saturation (CGC).

● Basic interest: unitarity in QCD andits phenomenological consequences,link with successful pre-QCD ideas(RFT, Glauber theory).

● Linear evolution equations: DGLAP or BFKL, modified to non-linearequations: JIMWLK, BK. Pioneering ideas in GLR, MQ:

1. Introduction: the MV setupN. Armesto

First correction to JIMWLK evolution from the classical EOMs 4

● McLerran-Venugopalan: valencequarks as sources for the classicaldynamics of slow partons. For highenough energies (and/or sizes),BFKL evolution drives the systemdense at any large scale:perturbative methods applicable.

● Effective FT: independence on the fast-slow separation scale gives arenormalization group equation (JIMWLK, Balitsky, Kovner-Lublinsky)

● Mean-field approximation: BK equation, well studied and understood.

2. The WF formalism: setupN. Armesto

First correction to JIMWLK evolution from the classical EOMs 5

● Evolution in the wave function of the projectile(Kovner, Wiedemann, '01; Kovner, Lublinsky, '05):superposition of fast gluons in the + direction

● Sab: single gluon scattering matrix, eikonal.

● Scattering matrix of the projectile: average over target configurations

● Evolution: small shift in rapidity,

● bi: WW fields of the projectile, solutions of the Yang-Mills EOMs.

(Sab=ab for initial,low density)

2. WF -> JIMWLK:N. Armesto

First correction to JIMWLK evolution from the classical EOMs 6

● Evolution for the weight functional:dipole model

● EOMs (MV, Kovchegov '96, '97): A+=0,

● To 1st order in g: JIMWLK

3. 1st corrections from EOMs:N. Armesto

First correction to JIMWLK evolution from the classical EOMs 7

● Limitations in JIMWLK: S's as c-numbers: high density target, andlowest order in g: dilute projectile --> asymmetric configuration (Kovner '05;Triantafyllopoulos '05, Soyez '06).

● Both problems linked, exact solution unknown:dense-dilute duality, 2-->1vertex, sFKPP equation...

● This work: higher order in gin the EOMs

3. 1st corr.: dipole modelN. Armesto

First correction to JIMWLK evolution from the classical EOMs 8

● Projectile made of dipoles:

LLL LLR

● Classifying in terms of the number ofdipoles:

: no leading 1/N correction to JIMWLK -> BK.

● Symmetry in the dipoles of the projectile allows further simplifications:complicated expressions in terms of higher poles, no projectile recombination.

4. Relevance for phenomenology: scaling?

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First correction to JIMWLK evolution from the classical EOMs 9

● Numerical studies needed to assess thepractical relevance of these correctionsfor e.g. the LHC: experimentalconsequences? Analogy with reaction-diffusion processes: sFKPP. ●Geometric scaling is a most compellingevidence of saturation (Stasto et al '00;Rummukainen et al '03; NA et al ‘04; Gelis etal '06).

• It appears naturally in the JIMWLKcontext, understood both analyticallyand numerically from the BK equation.●Correlations and pomeron loops(Mueller-Shoshi-Iancu-Munier '04)neglected in JIMWLK/BK, relevantfor dilute-dilute, break geometricscaling -> diffusive scaling (sFKPP)(Hatta et al '06).

LHC??

4. Relevance for phenomenology: correlations?

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● Analogy of QCD evolution to a reaction-diffusion process: old RFT is directedpercolation, similar to sFKPP (Iancu et al’06; Bondarenko et al ’06).● All this suggests searching the effects offluctuations or PhT on correlations.

● Rapidity correlations may help: try to identifydifferences between CGC predictions (no phasetransition without loops) (Kovchegov-Levin-McLerran-NA-Pajares '01, '06)

and those including a phase transition e.g. phenomenological models likepercolation, or realizations of dense-dense systems in hdQCD (Braun '00; ‘05).

B F

y2 y1

5. Summary:

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● JIMWLK evolution is suitable for dilute-dense scattering: correctionsneeded for less asymmetric situations.

● New ingredients proposed to mend this situation: correlations in thesource, pomeron loops in the evolution.

● We have analyzed the corrections to JIMWLK of order g coming fromhigher orders in the solution of the classical equations of motion for theslow glue:

* They give no correction to BK.* They cannot be expressed in terms of dipoles but givecontributions to higher correlators (in Balitsky hierarchy).

● Studies on the numerical/phenomenological relevance of these newingredients under development: correlations may offer an experimentaltesting ground at the LHC.

Backup I: complete expressionsN. Armesto

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Backup II: y-correlations in the CGCN. Armesto

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NA, McLerran, Pajares ’06 to appear in NPAUncorrelated diagram:

Correlated diagram:

● For gluons the long range rapidity correlation increases with energy,centrality and decreases with |y

1-y

2|. Baryons -> smaller correlation.

1/g

g

B F

y2 y1