The Color glass COndensate

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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
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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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STRUCTURE OF HIGHER ORDER CONTRIBUTIONS IN DIS
higher twist (power suppressed)
contributions

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

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

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DGLAP evolution Linear RG in Q2
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi
of gluons grows rapidly at small x
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Resolving the hadron -DGLAP evolution
increasing
But the phase space density decreases -the
proton becomes more dilute
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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
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QCD Bremsstrahlung
Proton
Proton is a dense many body system at high
energies
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Gribov,Levin,Ryskin Mueller, Qiu Blaizot, Mueller
Mechanism for parton saturation
Competition between attractive
bremsstrahlung and repulsive recombination
effects.
Maximal phase space density gt
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• Higher twists (power suppressed-in )
  
• are important when

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

Need a new organizing principle- beyond
the OPE- at small x.
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McLerran, RV Kovchegov Jalilian-Marian,Kovner,Mc
Lerran, Weigert
Born-Oppenheimer separation of large x and small
x modes
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

• Gluons are colored

• Random sources evolving on time scales much
  larger than natural time scales-very similar
  to spin glasses

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Quantum evolution of classical theory Wilsonian
RG
Sources
Fields
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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
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The hadron at high energies
Mean field solution of JIMWLK B-K equation
Balitsky-Kovchegov
DIS
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Evolution eqn. for the dipole cross-section
BK
Rapidity

• From saturation condition,

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How does Q_s behave as function of Y?
Fixed coupling LO BFKL
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Remarkable observation
Munier-Peschanski
B-K same universality class as FKPP
equation FKPP Fisher-Kolmogorov-Petrovsky-Piscu
nov
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 gt 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!
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Novel regime of QCD evolution at high energies
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Universality collinear versus k_t factorization
Collinear factorization
Di-jet production at colliders
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k_t factorization
Are these un-integrated gluon distributions
universal? Dipoles-with evolution a la JIMWLK
/ BK
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HADRONIC COLLISIONS IN THE CGC FRAMEWORK
Solve Yang-Mills equations for two light cone
sources
For observables
average over
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Systematic power counting-inclusive gluon
production
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

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Quark production to all orders in pA
Blaizot, Gelis, RV
3- 4- point operators More non-trivial
evolution with rapidity
Two point-dipole operator in nucleus
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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,
Wiedemann Blaizot, 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
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
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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 Romatschk
e, Strickland Jeon, RV, Weinstock
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Open questions

• 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?