From Glasma to Plasma

in Heavy Ion CollisionsRaju Venugopalan

Brookhaven National Laboratory

Topical Overview Talk, QM2008, Jaipur, Feb. 4th, 2008

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What is the Glasma ?

Glasma (\Glahs-maa\):

Noun: non-equilibrium matter between Color Glass Condensate (CGC)& Quark Gluon Plasma (QGP)

Ludlam, McLerran, Physics Today (2003)

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Why is the Glasma relevant ?

o Intrinsic interest:

The Glasma is key to quantitative understanding of matter produced in HI collisions

How does bulk matter flow in the Glasma influence transport in the perfect fluid ? How do jets interact with the Glasma ?

o Initial conditions for the QGP:

Glasma fields are among strongest Electric & Magnetic fields in nature. What are their properties ?

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Big Bang

CGC/Glasma

QGP

Little Bang

WMAP data(3x105 years)

Inflation

Hot Era

Plot by T. Hatsuda

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Big Bang vs. Little Bang

Decaying Inflaton field with occupation # 1/g2

Decaying Glasma field with occupation # 1/g2

Explosive amplification of low mom. small fluctuations (preheating)

Explosive amplification of low mom. small fluctuations (Weibel instability ?)

Interaction of fluct./inflaton - thermalization

Interaction of fluct./Glasma - thermalization ?

Other common features: topological defects, turbulence ?

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Before the Little Bang Nuclear wavefunction at high energies

Renormalization Group (JIMWLK/BK) equations sum leading logs

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αSY( )n

and high parton densities

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αSρ( )n

Successful CGC phenomenology of HERA e+p; NMC e+A; RHIC d+A & A+A

Review: RV, arXiv:0707.1867, DIS 2007

Bremsstrahlung

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∝αS

ln1

x

⎛

⎝ ⎜

⎞

⎠ ⎟

Recombination

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∝αSρ

+

= Saturation:

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E2 ~ B2 ~1

αS

αSY

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Hadron wave-fns: universal features

T. Ullrich (see talk) -based onKowalski, Lappi, RV ; PRL 100, 022303 (2008)

CGC Effective Theory= classic fields + strong stochastic sources

>> 1

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ρ ~1

g≈

1

αS

Upcoming test: current RHIC d+Au run - eg., forward di-jets (talk by C. Marquet)

Theory developments: running coupling in BKBalitsky;Albacete,Gardi,Kovchegov,Rummukainen,Weigert

αS(QS2) << 1

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How is Glasma formed in a Little Bang ?

Problem: Compute particle production in field theories with strong time dependent sources

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Glasma dynamics

perturbative vs non-perturbativeNon-perturbative for questions of interestin this talk

Interesting set of issues…not discussed here

(talks by Rajagopal and Iancu)

strong coupling vs weak coupling

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Systematic expansion for multiplicity moments

(=O(1/g2) and all orders in

(gρ)n)In QCD, solve Yang-Mills Eqns. for two nuclei

Glasma initial conditions frommatching classical CGCwave-fns on light coneKovner, McLerran, Weigert

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Numerical Simulations of

classical Glasma fields

LO Glasma fields are boost invariant

Krasnitz, Nara, RVLappi (see talk)

for

from extrapolating DIS data to RHIC energies

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LO Glasma MultiplicityAu-Au mult. at eta=0

Krasnitz, RV Kharzeev, Levin, Nardi

I) RHIC

II) LHC Pb+Pb at = 0≈ 950 - 1350 for Npart = 350(See Armesto talk for other LHC

predictions)Gelis,Stasto,RV

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Flow in the Glasma (I)• Large initial ET QS & NCGC Nhad consistent with strong isentropic flow. Initial conditions for hydro

Hirano, Nara

CGC- type initial conditions leave room for larger dissipation (viscosity) in hydro stage ?

Hirano et al., ; Drescher,NaraLappi, RV

• v2 (initial eccentricity)

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Flow in the Glasma (II)Partial thermalization and v2 fluctuations:

Bhalerao,Borghini,Blaizot,Ollitrault

Knudsen # K = /R with 1/K = cS dN/dy /area

Drescher,Dumitru,Gombeaud,Ollitrault

Partial thermalization fit suggests CGC gives lower v2 than Glauber

K0

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Flow in the Glasma (III)

o What’s the “pre-thermal” flow generated in the Glasma ?

Glasma v2

Krasnitz, Nara, RV: PLB 554, 21 (2003)

Glasma flow important for quantifying viscosity of sQGP

Classical field Classical field / Particle Particle

f < 1

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The unstable Glasma (I)

LO boost invariant E & B fields:- purely longitudinal for = 0+

- generate small amounts of topological charge

Kharzeev,Krasnitz,RVLappi,McLerran

pX,pY

pZ

Such configurations may lead to very anisotropic mom. dists. Weibel instability(see C. Greiner’s talk)

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The unstable Glasma (II)

• Small rapidity dependent quantum fluctuations of the LO Yang-Mills fields grow rapidly as

• E and B fields as large as EL and BL at time

increasing seed size

2500

Romatschke, RV:PRL,PRD(2006)

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The unstable Glasma (III)

Frequency of maximally unstablek mode grows rapidly

(Numerical studies by Frankfurt group - C. Greiner talk)

Romatschke, RV

Large angledeflections of coloredparticles in strong fields

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Small fluctuation spectrum

ab initio in the Glasma:

multiplicity moments to NLO

I) Anomalously low viscosityII) Large energy loss of jets in strong fields ?

Arnold, Moore; Mueller,Shoshi,Wong; Bödeker,Rummukainen

Turbulent isotropization on short time scales ?

(talks by Majumder and Müller)

III) Explosive generation of P and CP odd transitions via sphalerons (see Warringa’s talk)

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COBE FluctuationsCOBE Fluctuations

δt/t < 10-5, i.e. much smoother than a

baby’s bottom!

Another example of a small fluctuation spectrum…

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Multiplicity to NLO (=O(1) in g and all orders in (gρ)n )

+

Gluon pair production One loop contribution to classical field

Initial value problem with retarded boundary conditions- can be solved on a lattice in real time

Gelis, RV

(a la Gelis,Kajantie,Lappi for Fermion pair production)

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NLO and QCD Factorization

Gelis,Lappi,RV

What small fluctuations go into wave fn. and what go into particle production ?

Small x (JIMWLK)evolution of nucleus A -- sum (αSY)n terms

Small x (JIMWLK)evolution of nucleus B---sum (αSY)n terms

O(αS) but may

grow as

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From Glasma to Plasma NLO factorization formula:

With spectrum, can compute T - and match to hydro/kinetic theory

“Holy Grail” spectrum of small fluctuations. First computations and numerical simulations underway

Gelis,Fukushima,McLerranGelis,Lappi,RV

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Ridgeology** Rudy Hwa (see talk) + parallel session

Near side peak+ ridge (from talk by J. Putschke,STAR collaboration)Jet spectra Ridge spectra

pt,assoc,cutpt,assoc,cut

inclusive

inclusive

STAR preliminary STAR preliminary

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Two particle correlations in the Glasma: variance at

LO Gelis, RV: NPA 779 (2006), 177

Glasma sensitive to long range rapidity correlations:

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E pEqd2Ncorr.d3pd3q

∝d3k

(2π )32Ek∫ h−kh+k( ) • f (p) f (q)( )

Fourier modes of classical field: O(1/g)

Fourier modes of small fluctuation field: O(1)

(talk by Gelis)

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Our take on the RidgeGelis,Lappi,RV

i) Long range rapidity correlations built in at early times

because Glasma background field is boost invariant. (These are the “beam” jets.)

ii) Rapidity correlations are preserved because matter density dilutes rapidly along the beam direction

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Δφiii) Opacity effect in : Strong E & B fields destroy azimuthal correlations because survival probability of larger path lengths in radial direction is small (collimation a la Voloshin/Shuryak)

iv) May explain why features of the ridge persist for both soft and semi-hard associated particles

Need detailed models with realistic geometry effects

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Conclusions

I. Ab initio (NLO) calculations of the initial Glasma in HI collisions are becoming available

II. Quantifying how the Glasma thermalizes strongly constrains parameters of the (near) perfect fluid

III. Deep connections between QCD factorization and turbulent thermalization

IV. Possible explanation of interesting structures from jet+medium interactions