The quest for the holy Grail: from Glasma to Plasma

Raju Venugopalan

CATHIE-TECHQM workshop, Dec. 14-18, 2009

Color Glass

Condensates

Initial

Singularity

Glasma sQGP - perfect fluid

Hadron Gas

t

Nuclear wavefunction at high energies

At RHIC typical x ~ 0.01 . At the LHC, x ~ 5 * 10-4

PartonDensity

x= fraction of momentum of hadron carried by parton

Glue rules!

For glue, QS

2 = 1-1.4 GeV2 (RHIC)QS

2 = 2.6-4 GeV2 (LHC)

Kowalski,Lappi,RV, PRL (2008)

Nuclear wave function at high energies is a Color Glass Condensate

CGC: effective degrees of freedom

Fields Sources

€

x 1

Time dilated, “frozen” random color charges with weight W[]

Dynamical gauge fields

Classical eqns: RG eqn. for x evolution of source dist.: resums Sln(1/x) and /kT

2 contributions in loop corrections

Saturation scale QS: Non.Pert. scale in W at x0 grows with x evol. of RG

From CGC to Glasma

Multi-particle production from strong CGC fields:compute systematically properties of strongly correlated Glasma fields after collision

Consider T : At LO, can obtain from soln. of classical Yang-Mills eqns.

NLO terms are as large as LO for S ln(1/x) - resum to all ordersGelis,Lappi,RV (2008)

Glasma factorization => universal “density matrices W” calc. “matrix element”

<T> in the GlasmaAt RHIC energies, in central A+A, evolution of W’s is not significant - local Gaussian dist. of sources with variance QS

2 ; at LHC, evolution is very significantKrasnitz,Nara,RV (2003)

System initially very far from equilibrium! (Tzz <0 for =0+ and ->0 for > 1/QS)

Lappi,McLerran (2006)

Initial gauge field configurations are longitudinal chromo-electric & magnetic fields localized in transverse plane

- generate Chern-Simons charges0Kharzeev,Krasnitz,RV (2002)

Glasma flux tubes-IDumitru,Gelis,McLerran,RV (2008)

Conjecture based on pert. calculation:Glasma is a collection of “flux tubes” color screened on transverse distances ~ 1/QS

If conjecture is true, from geometry, must have

Non-perturbative (soln. of classical QCD!) computation of double inclusive gluon production in Glasma Lappi,Srednyak,RV:arXiv 0911.2068

Glasma flux tubes-II

Three possible scales for color screening: 1/R, m (QCD), QS

For 2 =1, (0.5-2) QS2

Color screening radius ~ 0.7-1.4 QS

Quantum evolution of distributions will give additional screening

Results of non-pert. computation confirm Glasma flux tube conjecture

Flux tube size in same ball park as experiments. Some variation in value depending on observable

Iancu,Itakura,McLerran (2002)A.H.Mueller (2003)

Long range rapidity correlations -> see Dusling talkarXiv:0911.2720

Matching Glasma dynamics to Hydro

Classical fieldClassical field / Particle Particle

f < 1

Current matching of LO Glasma YM computations to hydro - “CGC initial conditions”- assumes instantaneous thermalization

But T is far out of equilibrium in LO computations

No computations to date fully take into account NLO contributions that are as large as LO and should be resummed…

eccentricity

Unstable quanta in the GlasmaRomatschke,RV (2006)

Boost non-invariant quantum fluctuations can grow rapidlyfor > 0

for

Strong disordering could lead to rapid isotropization, “anomalous transport”

Asakawa,Bass,Muller (2006)Dumitru,Nara,Schenke,Strikland (2008)These quantum corrections, albeit difficult to

evaluate, are no less a necessary partof early time dynamics…

3+1-D YM simulations

Rapid isotropization in the Glasma

Resum - extend range of YM-dynamics

“Holy Grail” Spectrum of small fluctuations

Fukushima,Gelis,McLerran (2006)

Gelis,Lappi,RV (2008)

Can also compute event by event initial conditions to estimate flow fluctuations:

Similar in spirit to the event by event hydro code

NeXSPheRIO = NeXus + SPheRIO Grassi et al., arXiv:0912.0703

Summary

The early time dynamics of HI collisions can be computed ab initio in a factorization framework

Early time Yang-Mills dynamics reveals structure of the Glasma as a collection of flux tubes color screened on distances ~ 1/QS

Quantum instabilities from the wave-function can lead to early isotropization; significant effects on final states

The factorization framework for n-point correlations is ideally suited to event-by-event analysis

Many interesting conceptual issues in understanding the Glasma -> sQGP transition