From Glasma to Plasma in Heavy Ion Collisions Raju Venugopalan Brookhaven National Laboratory Topical Overview Talk, QM2008, Jaipur, Feb. 4th, 2008
Jan 20, 2016
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