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The 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…
STRUCTURE OF HIGHER ORDER CONTRIBUTIONS IN DIS
+ higher twist (power suppressed)
contributions…
 Coefficient functions - C - computed to NNLO for many pr
e.g., gg -> H
Harlander, Kilgore; Ravindran,Van Neerven,Smith; …
 Splitting functions -P - computed to 3-loops recently!
Moch, Vermaseren, Vogt
DGLAP evolution: Linear RG in Q^2
Dokshitzer-Gribov-Lipatov-Altarelli-Par
# of gluons grows rapidly at small x…
Resolving the hadron
-DGLAP evolution
increasing
But… the phase space density decreases
-the proton becomes more dilute
The other interesting limit-is the Regge
limit of QCD:
Physics of strong fields in QCD, multi-particle productionpossibly discover novel universal properties of theory in this lim
BFKL evolution: Linear RG in x
Balitsky-Fadin-Kuraev-Lipatov
- Large x
- Small x
Gluon density saturates at f=
Non-linear evolution:
Gluon recombination
QCD
Bremsstrahlung
Proton
Proton is a dense many body system at high energies
Mechanism for parton saturation:
Gribov,Levin,Ryskin
Mueller, Qiu
Blaizot, Mueller
Competition between “attractive” bremsstrahlung
and “repulsive” recombination effects.
Maximal phase space density =>
Saturated for
 Higher twists (power suppressed-in
)
are important when:
 Leading twist “shadowing’’ of these contributions c
extend up to
at small x.
Need a new organizing principlebeyond the OPE- at small x.
McLerran, RV; Kovchegov;
Jalilian-Marian,Kovner,McLerran, Weige
Born-Oppenheimer: separation of large x and small x modes
Dynamical
Wee modes
Valence
modes-are
static sources
for wee
modes
In large nuclei, sources are Gaussian random sources
MV,
Kovchegov,
Jeon,
Hadron at high energies is a Color Glass Condensate
 Gluons are colored
 Random sources evolving on time scales much larger
than natural time scales-very similar to spin glasses
 Bosons with large occupation # ~
 Typical momentum of gluons is
- form a condensate
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.
Rummukainen, Weigert
 Mean field approximation of hierarchy in large
N_c and large A limit- the BK equation.
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
Rapidit
y:
1
1/2
 From saturation condition,
How does Q_s behave as function of Y?
Fixed coupling LO BFKL:
LO BFKL+ running coupling:
Re-summed NLO BFKL + CGC:
Triantafyllopolous
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Very close to
HERA 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. Saarlos
D. 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
Collinear factorization:
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Di-jet production at colliders
k_t factorization:
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Are these “un-integrated gluon distributions” universal?
“Dipoles”-with evolution a la JIMWLK / BK
HADRONIC COLLISIONS IN THE CGC FRAMEWORK
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Solve Yang-Mills equations for two light cone sources:
For observables
average over
Systematic power counting-inclusive gluon production
Breaks down at next order
in
Krasnitz,RV;
Balitsky
Adjoint dipole
-includes all twists
 K_t factorization seen “trivially” in p-p
 Also holds for inclusive gluon production
lowest order in
but all orders
in
Quark production to all orders in pA
Blaizot,
Gelis, RV
3- & 4- point operators
Two point-dipole
operator in nucleus
More non-trivial evolution
with rapidity…
The demise of the Structure function
 Dipoles (and multipole) operators may be more
relevant observables at high energies
Jalilian-Marian, Gelis;
Kovner, Wiedemann
Blaizot, Gelis, RV
 Are universal-process independent.
 RG running of these operators - detailed tests of
high energy QCD.
Strong hints of the CGC from
Deuteron-Gold data at RHIC
Colliding Sheets of Colored Glass at High Energies
Krasnitz,Nara,RV;
Lappi
Classical Fields with occupation # f=
Initial energy and multiplicity of produced gluons
depends on Q_s
Straight forward extrapolation from HERA: Q_s = 1.4 GeV
McLerran,
Ludlam
In bottom up scenario,
~ 2-3 fm at RHIC
Baier,Mueller,Schiff,Son
Exciting possibility - non-Abelian “Weibel” instabilities
speed up thermalization - estimates: Isotropization time
~ 0.3 fm
~
Mrowczynski;
Arnold,Lenaghan,Moore,Yaffe
Romatschke, Strickland; Jeon, RV,
 Are there contributions in high energy QCD beyond JIMWL
 Are “dipoles” the correct degrees of freedom at high energi
 Do we have a consistent phenomenological picture?
 Can we understand thermalization from first principles?