The Color glass COndensateThe Color glass COndensate

A classical effective theory of high energy QCD

Raju Venugopalan

Brookhaven National Laboratory

ICPAQGP, Feb. 8th-12th, 2005

Outline of talk:

Introduction

A classical effective theory (and its quantum evolution) for high energy QCD Hadronic scattering and k_t factorization in the Color Glass Condensate

What the CGC tells us about the matter produced in dA and AA collisions at RHIC.

Open issues

Much of the discussion in pQCD has focused on the Bjorken limit:

Asymptotic freedom, the Operator Product Expansion (OPE) & Factorization Theorems:

machinery of precision physics in QCD…

Coefficient functions - C - computed to NNLO for many processes, e.g., gg -> H Harlander, Kilgore; Ravindran,Van Neerven,Smith; …

Splitting functions -P - computed to 3-loops recently! Moch, Vermaseren, Vogt

+ higher twist (power suppressed) contributions…

STRUCTURE OF HIGHER ORDER CONTRIBUTIONS IN DIS

DGLAP evolution: Linear RG in Q^2Dokshitzer-Gribov-Lipatov-Altarelli-Parisi

# of gluons grows rapidly at small x…

increasing

But… the phase space density decreases-the proton becomes more dilute

Resolving the hadron -DGLAP evolution

The other interesting limit-is the Regge limit of QCD:

Physics of strong fields in QCD, multi-particle production- possibly discover novel universal properties of theory in this limit

- Large x

- Small x

Gluon density saturates at f=

BFKL evolution: Linear RG in xBalitsky-Fadin-Kuraev-Lipatov

Proton

Proton is a dense many body system at high energies

QCD Bremsstrahlung

Non-linear evolution:Gluon recombination

Mechanism for parton saturation:

Competition between “attractive” bremsstrahlungand “repulsive” recombination effects.

Maximal phase space density =>

Saturated for

Gribov,Levin,RyskinMueller, QiuBlaizot, Mueller

Need a new organizing principle-beyond the OPE- at small x.

Higher twists (power suppressed-in ) are important when:

Leading twist “shadowing’’ of these contributions can extend up to at small x.

Born-Oppenheimer: separation of large x and small x modes

DynamicalWee modes

Valence modes-are static sources for wee modes

McLerran, RV; Kovchegov;Jalilian-Marian,Kovner,McLerran, Weigert

In large nuclei, sources are Gaussian random sources MV, Kovchegov, Jeon, RV

Hadron at high energies is a Color Glass Condensate

Random sources evolving on time scales much larger than natural time scales-very

similar to spin glasses

Typical momentum of gluons is

Bosons with large occupation # ~ - form a condensate

Gluons are colored

Quantum evolution of classical theory: Wilsonian RG

Fields Sources

Integrate out Small fluctuations => Increase color charge of sources

JIMWLK(Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner)

JIMWLK RG Eqns. Are master equations-a la BBGKY hierarchy in Stat. Mech. -difficult to solve

Preliminary numerical studies.

Mean field approximation of hierarchy in large N_c and large A limit- the BK equation.

Rummukainen, Weigert

Balitsky; Kovchegov

The hadron at high energies

Mean field solution of JIMWLK = B-K equation

Balitsky-Kovchegov

DIS:

Dipole amplitude N satisfies BFKL kernel

BK: Evolution eqn. for the dipole cross-section

From saturation condition,

1

1/2

Rapidity:

How does Q_s behave as function of Y?

Fixed coupling LO BFKL:

LO BFKL+ running coupling:

Re-summed NLO BFKL + CGC:

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Triantafyllopolous

Very close toHERA result!

Remarkable observation: Munier-Peschanski

B-K same universality class as FKPP equation

FKPP = Fisher-Kolmogorov-Petrovsky-Piscunov

FKPP-describes travelling wave fronts - B-K “anomalous dimensions” correspond to spin glass phase of FKPP

Stochastic properties of wave fronts => sFKPP equation

W. SaarlosD. Panja

Exciting recent development: Can be imported from Stat. Mech to describe fluctuations (beyond B-K) in high energy QCD.

Tremendous ramifications for event-by-event studies At LHC and eRHIC colliders!

Novel regime of QCD evolution at high energies

“Higher twists”

Leading twist shadowing

Universality: collinear versus k_t factorization

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Collinear factorization:

Di-jet production at colliders

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.k_t factorization:

Are these “un-integrated gluon distributions” universal?

“Dipoles”-with evolution a la JIMWLK / BK

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Solve Yang-Mills equations for two light cone sources:

For observables average over

HADRONIC COLLISIONS IN THE CGC FRAMEWORK

K_t factorization seen “trivially” in p-p

Also holds for inclusive gluon production lowest order in but all orders in

Adjoint dipole-includes all twists

Breaks down at next order in

Krasnitz,RV; Balitsky

Systematic power counting-inclusive gluon production

Quark production to all orders in pABlaizot,Gelis, RV

Two point-dipole operator in nucleus

3- & 4- point operators

More non-trivial evolution with rapidity…

The demise of the Structure function

Dipoles (and multipole) operators may be more relevant observables at high energies

Are universal-process independent.

RG running of these operators - detailed tests of high energy QCD.

Jalilian-Marian, Gelis;Kovner, WiedemannBlaizot, Gelis, RV

Strong hints of the CGC from Deuteron-Gold data at RHIC

Colliding Sheets of Colored Glass at High Energies

Classical Fields with occupation # f=

Initial energy and multiplicity of produced gluonsdepends on Q_s

Krasnitz,Nara,RV;

Lappi

Straight forward extrapolation from HERA: Q_s = 1.4 GeV

McLerran,Ludlam

In bottom up scenario, ~ 2-3 fm at RHICBaier,Mueller,Schiff,Son

Exciting possibility - non-Abelian “Weibel” instabilities speed up thermalization - estimates: Isotropization time ~ ~ 0.3 fm

Mrowczynski; Arnold,Lenaghan,Moore,YaffeRomatschke, Strickland; Jeon, RV, Weinstock

Are there contributions in high energy QCD beyond JIMWLK?

Are “dipoles” the correct degrees of freedom at high energies?

Do we have a consistent phenomenological picture?

Can we understand thermalization from first principles?