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

2. What is the Glasma ? Glasma (\Glahs-maa\):
Ludlam, McLerran, Physics Today (2003)
Glasma (\Glahs-maa\):
Noun: non-equilibrium matter
between Color Glass Condensate (CGC)
& Quark Gluon Plasma (QGP)

3. Why is the Glasma relevant ?
Intrinsic interest:
Glasma fields are among strongest
Electric & Magnetic fields in nature.
What are their properties ?
How does bulk matter flow in the Glasma
influence transport in the perfect fluid ?
How do jets interact with the Glasma ?
Initial conditions for the QGP:
The Glasma is key to quantitative understanding
of matter produced in HI collisions

4. Big Bang Little Bang Hot Era QGP Inflation CGC/ Glasma
WMAP data
(3x105 years)
QGP
Inflation
CGC/
Glasma
Plot by T. Hatsuda

5. Big Bang vs. Little Bang
Decaying Inflaton field
with occupation # 1/g2
Decaying Glasma field
Explosive amplification
of low mom. small
fluctuations (preheating)
fluctuations (Weibel instability ?)
Interaction of fluct./inflaton
- thermalization
Interaction of fluct./Glasma
- thermalization ?
Other common features: topological defects, turbulence ?

6. Before the Little Bang + Nuclear wavefunction at high energies  SY
Bremsstrahlung
 SY +
Recombination
= Saturation:
Renormalization Group (JIMWLK/BK) equations sum
leading logs
and high parton densities
Successful CGC phenomenology of HERA e+p; NMC e+A;
RHIC d+A & A+A
Review: RV, arXiv: , DIS 2007

7. Hadron wave-fns: universal features
CGC Effective Theory
= classic fields + strong
stochastic sources
>> 1
S(QS2) << 1
T. Ullrich (see talk) -based on
Kowalski, Lappi, RV ; PRL 100, (2008)
Theory developments: running coupling in BK
Balitsky;Albacete,Gardi,Kovchegov,Rummukainen,Weigert
Upcoming test: current RHIC d+Au run - eg., forward di-jets
(talk by C. Marquet)

8. How is Glasma formed in a Little Bang ?
Problem: Compute particle production in field
theories with strong time dependent sources

9. Glasma dynamics perturbative vs non-perturbative
for questions of interest
in this talk
perturbative vs non-perturbative
Interesting set of issues…not discussed here
(talks by Rajagopal and Iancu)
strong coupling vs weak coupling

10. Systematic expansion for multiplicity moments
(=O(1/g2) and all orders in (g)n)
In QCD, solve Yang-Mills Eqns. for two nuclei
Glasma initial conditions from
matching classical CGC
wave-fns on light cone
Kovner, McLerran, Weigert

11. Numerical Simulations of classical Glasma fields
Krasnitz, Nara, RV
Lappi (see talk)
LO Glasma fields are boost invariant
for
from extrapolating DIS data to RHIC energies

12. LO Glasma Multiplicity
I) RHIC
Au-Au mult. at eta=0
Krasnitz, RV
Kharzeev, Levin, Nardi
II) LHC
Pb+Pb at  = 0
≈ for Npart = 350
(See Armesto talk for
other LHC predictions)
Gelis,Stasto,RV

13. Flow in the Glasma (I) v2   (initial eccentricity)
Large initial ET  QS & NCGC  Nhad consistent
with strong isentropic flow. Initial conditions for hydro
Hirano, Nara
Hirano et al., ; Drescher,Nara
Lappi, RV
v2   (initial eccentricity)
CGC- type initial conditions leave room
for larger dissipation (viscosity) in hydro stage ?

14. 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
K0

15. Flow in the Glasma (III)
What’s the “pre-thermal” flow generated in the Glasma ?
Classical field
Classical field / Particle
Particle
f < 1
Glasma v2
Krasnitz, Nara, RV: PLB 554, 21 (2003)
Glasma flow important for
quantifying viscosity of sQGP

16. The unstable Glasma (I)
Kharzeev,Krasnitz,RV
Lappi,McLerran
LO boost invariant E & B fields:
purely longitudinal for  = 0+
generate small amounts of topological charge
pX,pY pZ
Such configurations may lead to very
anisotropic mom. dists.  Weibel instability
(see C. Greiner’s talk)

17. 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
Romatschke, RV:PRL,PRD(2006)
increasing
seed size
2500

18. The unstable Glasma (III)
Romatschke, RV
Frequency of
maximally unstable
k mode grows rapidly
Large angle
deflections of colored
particles in strong fields
(Numerical studies by
Frankfurt group - C. Greiner talk)

19. Turbulent isotropization on short time scales ?
Arnold, Moore; Mueller,Shoshi,Wong;
Bödeker,Rummukainen
I) Anomalously low viscosity II) Large energy loss of jets in strong fields ?
(talks by Majumder and Müller)
III) Explosive generation of P and CP odd transitions
via sphalerons (see Warringa’s talk)
Small fluctuation spectrum ab initio in the Glasma: multiplicity moments to NLO

20. Another example of a small fluctuation spectrum…

21. Multiplicity to NLO + (=O(1) in g and all orders in (g)n )
Gelis, RV +
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
(a la Gelis,Kajantie,Lappi for Fermion pair production)

22. 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 (SY)n terms
O(S) but may
grow as
Small x (JIMWLK)
evolution of nucleus B
---sum (SY)n terms

23. From Glasma to Plasma NLO factorization formula:
“Holy Grail” spectrum of small fluctuations.
First computations and numerical simulations underway
Gelis,Fukushima,McLerran
Gelis,Lappi,RV
With spectrum, can compute T - and match to
hydro/kinetic theory

24. Ridgeology*
* Rudy Hwa (see talk)
+ parallel session
Near side peak+ ridge (from talk by J. Putschke,STAR collaboration)
Jet spectra
Ridge spectra
STAR preliminary
STAR preliminary
inclusive
inclusive
pt,assoc,cut
pt,assoc,cut

25. Two particle correlations in the Glasma: variance at LO
Gelis, RV: NPA 779 (2006), 177
Glasma sensitive to long range rapidity correlations:
Fourier modes of
classical field: O(1/g)
Fourier modes of small
fluctuation field: O(1)
(talk by Gelis)

26. Our take on the Ridge
Gelis,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
iii) 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

27. Conclusions in HI collisions are becoming available
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