Strong gluon fields
in nucleons & nuclei
Raju Venugopalan
Brookhaven National Laboratory
EIC meeting, Hampton Univ., May 19th-23rd, 2008
Talk Outline
 The CGC and the nuclear “oomph”
 From CGC to Glasma: high energy
factorization
 Some remarkable features of the
Glasma
2
The Bjorken limit
• Operator product expansion (OPE),
Factorization theorems,
machinery of precision physics in QCD
3
The Regge-Gribov limit
• Physics of strong fields in QCD,
Multi-particle production,
Novel universal properties of QCD ?
4
Mechanism of gluon saturation
Gribov,Levin,Ryskin
Mueller,Qiu
Large x - bremsstrahlung
linear evolution (DGLAP/BFKL)
Small x -gluon recombination
non-linear evolution
(BK/JIMWLK)
p, A
Saturation scale QS(x) - dynamical scale below
which non-linear (“higher twist”) QCD dynamics
is dominant
5
The Color Glass Condensate
McLerran, RV
Iancu, Leonidov,McLerran
In the saturation regime:
Strongest fields in nature!
CGC: Classical effective theory of QCD describing
dynamical gluon fields + static color sources in nonlinear regime
o
Renormalization group equations (JIMWLK/BK)
describe how the QCD dynamics changes with energy
o
A universal saturation scale QS arises naturally in the theory
6
Saturation scale grows with energy
Typical gluon
momenta are large
Typical gluon kT in
hadron/nuclear
wave function
Bulk of high energy cross-sections:
a) obey dynamics of novel non-linear
QCD regime
b) Can be computed systematically in
weak coupling
7
Nuclear “Oomph”:Saturation scale grows with A
High energy compact (1/Q < Rp) probes interact coherently across
nuclear size 2 RA - experience large field strengths
Extension of dipole models to nuclei
Kowalski, Teaney, PRD68 (2003)
Kowalski, Lappi, RV, PRL100 (2008)
Resulting A dependence
of QS2 ~ A1/3
8
Nuclear “oomph” (II): Diffractive DIS
Kowalski,Lappi,Marquet,RV (2008)
Very large fraction of e+A events (~ 25%) are diffractive*
- nucleus either intact (“non breakup”)
or breaks up into nucleons separated from
the hadronic final state by a large rapidity gap
* Results broadly agree on large magnitude of effect with other models albeit details may vary
9
Hadron wave-fns: universal features
9 for glue

4
S(QS2) << 1

T. Ullrich
Note: Strong constraints from RHIC A+A: Nch ~ QS2 and
ET ~ QS3 - “day 1” A+A at LHC will provide important confirmation
 Careful analysis gives values consistent with above
plot to ~15% T. Lappi, arXiv:07113039 [hep-ph]
10
Can we learn something from the AdS-CFT (QCD) about possible
universality between weak coupling strong fields &
QCD at strong coupling ?
 Remarkably, many results expressed in terms of QS appear
universal (see following talk by Sabio Vera)
11
Glasma
Ludlam, McLerran, Physics Today (2003)
Glasma (\Glahs-maa\):
Noun: non-equilibrium matter
between Color Glass Condensate (CGC)
& Quark Gluon Plasma (QGP)
12
Little Bang
Big Bang
WMAP data
Hot Era
(3x105 years)
Inflation
QGP
CGC/
Glasma
Plot by T. Hatsuda
13
How is Glasma formed in a Little Bang ?
 Problem: Compute particle production in field
theories with strong time dependent sources
14
NLO and QCD Factorization
Gelis,Lappi,RV
What small fluctuations go into wave fn. arXiv:0804.2630 [hep-ph]
and what go into particle production ?
Small x (JIMWLK)
evolution of nucleus A
-- sum (SY)n & (S 1)n
terms
O(S) but may
grow as
Small x (JIMWLK)
evolution of nucleus B
---sum (SY)n & (S 2)n terms
15
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
16
Relating the Glasma to the wavefunction
 The Ridge in two particle correlations
 P and CP violation in heavy ion collisions
 Elliptic flow & flow fluctuations
17
Two particle correlations in the Glasma
Can it explain the near side ridge ?
18
Ridgeology* * Rudy Hwa
Near side peak+ ridge (from talk by J. Putschke,STAR collaboration)
Jet spectra
STAR preliminary
Ridge spectra
STAR preliminary
inclusive
inclusive
19
pt,assoc,cut
pt,assoc,cut
Evolution of mini-jet with centrality
Same-side peak
83-94%
Little shape change from
peripheral to 55% centrality
55-65%
46-55%
Large change
within ~10%
centrality
0-5%
Smaller change from
transition to most central
Binary scaling reference followed until sharp transition at ρ ~ 2.5
~30% of the hadrons in central Au+Au participate in the same-side correlation
M. Daugherty Session IX, QM2008
20
Update: the ridge comes into its own
PHENIX: sees a ridge
Au+Au 200 GeV, 0 - 30%
PHOBOS preliminary
1
Ntrig
d2Nch
dd
PHOBOS: the ridge extends to
very high rapidity
21
For particles to have been emitted from the same
Event Horizon, causality dictates that
If Y is as large as (especially) suggested by
PHOBOS, correlations were formed very early
- in the Glasma…
22
An example of a small fluctuation spectrum…
COBE Fluctuations
t/t
< 10-5,
i.e. much smoother than a
baby’s bottom!
23
Z
Z
T
T
After a HI collision, classical fields form a
Glasma flux tube with longitudinal chromo E & B fields
Typical size of flux tube
in transverse direction is
1 / QS < 1/QCD
24
2 particle correlations in the Glasma (I)
Dumitru, Gelis ,McLerran, RV, arXiv:0804.3858[hep-ph]]
=
+
Leading (classical) contribution
Note: Interestingly, computing leading logs to all orders, both
diagrams can be expressed as the first diagram with
sources evolved a la JIMWLK Hamiltonian
Gelis, Lappi, RV (2008)
25
2 particle spectrum (II)
Simple “Geometrical” result:
  4 (more accurate result requires numerical
soln. of YM eqns. - in progress.
with K_N  0.3
26
2 particle spectrum (III)
Not the whole story… particle emission from the Glasma
tubes is isotropic in the azimuth
Particles correlated by transverse flow (or at high pT by
opacity effects) - are highly localized
transversely, experience same transverse boost
Voloshin, Shuryak
Gavin, Pruneau, Voloshin
Vr

1
QS
R

27
Ridge from flowing Glasma tubes
KN ~ 0.1
Gets many features right:
i) Same flavor composition as bulk matter
(energy & centrality dep.
of flow courtesy of
Paul Sorensen)
ii) Large multiplicity (1/3rd) in the Ridge relative to the bulk
iii) Ridge independent of trigger pT-geometrical effect
iv) Signal for like and unlike sign pairs the same at large 
28
P and CP violation in the Glasma
Kharzeev; Kharzeev, McLerran, Warringa
Gluons
Quarks
Lagrangean invariant under scale (dilatations) and chiral
( Left
Right ) transformations for massless quarks
Both symmetries
broken by quantum
effects
- anomalies
29
QCD vacuum and sphaleron transitions
Vacua labeled by different
Chern-Simons # 
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
EB
“Over the barrier” sphaleron transitions can change the
topological charge in an event => the index theorem tells us that
this induces a induce a net chirality.
(Note: Sphaleron transitions at the Electroweak Transition
are a candidate for generating matter-anti-matter
asymmetry in the universe)
30
Real time Chern-Simons diffusion
In the Glasma
Kharzeev, Krasnitz, RV, Phys. Lett. B545 (2002)
At finite T
Arnold, Moore, PRD73 (2006)
31
The Chiral Magnetic effect in the Glasma
Kharzeev,McLerran,Warringa, 0711.0950
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Heavy Ion Collisions at RHIC: Largest
Terrestrial magnetic fields!
32
Magnetic fields + Sphaleron transitions
= Chiral Magnetism
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Red arrow - momentum; blue arrow - spin;
In the absence of topological charge no asymmetry between left and
right (fig.1) ;the fluctuation of topological charge (fig.2) in the presence
of magnetic field induces electric current (fig.3)
33
Measuring charge asymmetry
S.Voloshin, hep-ph/0406311
+
m
- k
Preliminary STAR result
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
S. Voloshin et al [STAR Coll.], QM’08
I. Selyuzhenkov et al., STAR Coll., nucl-ex/0510069
34
Summary
 Non-linear dynamics of QCD strongly
enhanced in nuclei
 Factorization theorems linking these strong fields
in the wavefunction to early time dynamics
(Glasma) are becoming available
 These strong fields have important
consequences and may explain recent
remarkable data from RHIC
35
Extra Slides
36
2 particle spectrum…
Centrality dependence of Vr from blast wave fits
Centrality dependence of QS a la Kharzeev-Nardi
37