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