strong gluon fields in nucleons & nuclei raju venugopalan brookhaven national laboratory eic...
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Strong gluon fields in nucleons & nuclei
Raju Venugopalan
Brookhaven National Laboratory
EIC meeting, Hampton Univ., May 19th-23rd, 2008
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Talk Outline
The CGC and the nuclear “oomph”
From CGC to Glasma: high energy
factorization
Some remarkable features of the Glasma
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The Bjorken limit
• Operator product expansion (OPE), Factorization theorems, machinery of precision physics in QCD
4
The Regge-Gribov limit
• Physics of strong fields in QCD, Multi-particle production, Novel universal properties of QCD ?
5
Mechanism of gluon saturation
p, A
Large x - bremsstrahlunglinear evolution (DGLAP/BFKL)
Small x -gluon recombinationnon-linear evolution(BK/JIMWLK)
Saturation scale QS(x) - dynamical scale below which non-linear (“higher twist”) QCD dynamics is dominant
Gribov,Levin,RyskinMueller,Qiu
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CGC: Classical effective theory of QCD describingdynamical gluon fields + static color sources in non-linear 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
The Color Glass Condensate
In the saturation regime:
Strongest fields in nature!
McLerran, RVIancu, Leonidov,McLerran
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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 regimeb) Can be computed systematically in
weak coupling
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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
Resulting A dependenceof QS
2 ~ A1/3
Kowalski, Teaney, PRD68 (2003)Kowalski, Lappi, RV, PRL100 (2008)
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Nuclear “oomph” (II): Diffractive DISKowalski,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
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Hadron wave-fns: universal features
T. Ullrich
S(QS2) << 1
€
×9
4for glue
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]
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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)
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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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Big Bang
CGC/Glasma
QGP
Little Bang
WMAP data(3x105 years)
Inflation
Hot Era
Plot by T. Hatsuda
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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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NLO and QCD Factorization
Gelis,Lappi,RVarXiv:0804.2630 [hep-ph]What small fluctuations go into wave fn.
and what go into particle production ?Small x (JIMWLK)evolution of nucleus A -- sum (SY)n & (S 1)n
terms
Small x (JIMWLK)evolution of nucleus B---sum (SY)n & (S 2)n terms
O(S) 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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Relating the Glasma to the wavefunction
The Ridge in two particle correlations
P and CP violation in heavy ion collisions
Elliptic flow & flow fluctuations
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Two particle correlations in the Glasma
Can it explain the near side ridge ?
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Ridgeology** Rudy Hwa
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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Same-side peak
Little shape change from peripheral to 55% centrality
83-94% 55-65%
ηΔ width
STAR Preliminary
STAR Preliminary
Large change within ~10%
centrality
46-55%
STAR Preliminary
Smaller change from transition to most central
0-5%
STAR Preliminary
Evolution of mini-jet with centrality
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
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Update: the ridge comes into its own
PHOBOS: the ridge extends to very high rapidity
PHENIX: sees a ridge
Au+Au 200 GeV, 0 - 30%PHOBOS preliminary
ηΔφΔ dd
Nd
N
1 ch2
trig
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For particles to have been emitted from the same Event Horizon, causality dictates that
If ΔY is as large as (especially) suggested byPHOBOS, correlations were formed very early- in the Glasma…
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COBE FluctuationsCOBE Fluctuations
δt/t < 10-5, i.e. much smoother than a
baby’s bottom!
An example of a small fluctuation spectrum…
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ZZ
TT
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
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2 particle correlations in the Glasma (I)
+=
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)
Dumitru, Gelis ,McLerran, RV, arXiv:0804.3858[hep-ph]]
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2 particle spectrum (II)
Simple “Geometrical” result:
4 (more accurate result requires numerical soln. of YM eqns. - in progress.
with K_N 0.3
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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
R€
1
QS
€
Vr
Voloshin, ShuryakGavin, Pruneau, Voloshin
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Ridge from flowing Glasma tubes
KN ~ 0.1(energy & centrality dep.of flow courtesy of Paul Sorensen)Gets many features right:
i) Same flavor composition as bulk matterii) Large multiplicity (1/3rd) in the Ridge relative to the bulkiii) Ridge independent of trigger pT-geometrical effectiv) Signal for like and unlike sign pairs the same at large Δη
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P and CP violation in the Glasma
Gluons Quarks
Lagrangean invariant under scale (dilatations) and chiral
RightLeft ) transformations for massless quarks(
Both symmetriesbroken by quantumeffects - anomalies
Kharzeev; Kharzeev, McLerran, Warringa
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QCD vacuum and sphaleron transitions
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Vacua labeled by different Chern-Simons #
“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.
EB
(Note: Sphaleron transitions at the Electroweak Transition are a candidate for generating matter-anti-matter asymmetry in the universe)
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Real time Chern-Simons diffusion
Kharzeev, Krasnitz, RV, Phys. Lett. B545 (2002) Arnold, Moore, PRD73 (2006)
In the Glasma At finite T
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The Chiral Magnetic effect in the GlasmaKharzeev,McLerran,Warringa, 0711.0950
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Heavy Ion Collisions at RHIC: Largest Terrestrial magnetic fields!
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Magnetic fields + Sphaleron transitions = Chiral Magnetism
QuickTime™ and aTIFF (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)
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Measuring charge asymmetry
+
-
m
k
S.Voloshin, hep-ph/0406311
QuickTime™ and aTIFF (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
Preliminary STAR result
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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
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Extra Slides
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2 particle spectrum…
Centrality dependence of Vr from blast wave fitsCentrality dependence of QS a la Kharzeev-Nardi