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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 - PowerPoint PPT Presentation
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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
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?