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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
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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
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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…
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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
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DGLAP evolution: Linear RG in Q^2Dokshitzer-Gribov-Lipatov-Altarelli-Parisi
# of gluons grows rapidly at small x…
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increasing
But… the phase space density decreases-the proton becomes more dilute
Resolving the hadron -DGLAP evolution
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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
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- Large x
- Small x
Gluon density saturates at f=
BFKL evolution: Linear RG in xBalitsky-Fadin-Kuraev-Lipatov
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Proton
Proton is a dense many body system at high energies
QCD Bremsstrahlung
Non-linear evolution:Gluon recombination
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Mechanism for parton saturation:
Competition between “attractive” bremsstrahlungand “repulsive” recombination effects.
Maximal phase space density =>
Saturated for
Gribov,Levin,RyskinMueller, QiuBlaizot, Mueller
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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.
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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
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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
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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)
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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
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The hadron at high energies
Mean field solution of JIMWLK = B-K equation
Balitsky-Kovchegov
DIS:
Dipole amplitude N satisfies BFKL kernel
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BK: Evolution eqn. for the dipole cross-section
From saturation condition,
1
1/2
Rapidity:
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How does Q_s behave as function of Y?
Fixed coupling LO BFKL:
LO BFKL+ running coupling:
Re-summed NLO BFKL + CGC:
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Triantafyllopolous
Very close toHERA result!
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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
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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!
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Novel regime of QCD evolution at high energies
“Higher twists”
Leading twist shadowing
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Universality: collinear versus k_t factorization
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Collinear factorization:
Di-jet production at colliders
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QuickTime™ and aTIFF (LZW) decompressor
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Are these “un-integrated gluon distributions” universal?
“Dipoles”-with evolution a la JIMWLK / BK
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Solve Yang-Mills equations for two light cone sources:
For observables average over
HADRONIC COLLISIONS IN THE CGC FRAMEWORK
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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
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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…
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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
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Strong hints of the CGC from Deuteron-Gold data at RHIC
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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
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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
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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?