Universal features of QCD dynamics in hadrons & nuclei at high energies

Raju VenugopalanBrookhaven National Laboratory

TIFR, Mumbai, Feb. 12th-14th, 2008

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Outline of Talk

o CGC-brief overview

o The CGC and DIS

o Dipole models and RHIC data

o Open questions/future work

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CGC: Classical effective theory of QCD describingdynamical gluon fields + static color sources in non-linear regime

o Novel 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

Bulk of high energy cross-sections:a) obey dynamics of novel non-linear QCD regimeb) Can be computed systematically in weak coupling

Typical gluon kT in hadron/nuclear wave function

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Saturation scale grows with A

High energy compact (1/Q < Rp) probes interact coherently across

nuclear size 2 RA - experience large field strengths

Enhancement of QS with A => non-linear QCD regime reached at significantly lower energy in A than in proton

Pocket formula:

Pocket formula holds up under detailed analysisKowalski, Lappi, RV

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New window on universal properties of the matter in nuclear wavefunctions

A

Can we quantify the various regimes ?

Iancu, RV, hep-ph/0303204

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DIS

sy

Q

pq

Qx

E

E

pk

pqy

EEQ

kkqQ

e

e

e

eee

22

2

22

222

2

2cos1

2sin4

)(

==

⎟⎠⎞

⎜⎝⎛ ′′

−==

⎟⎠⎞

⎜⎝⎛ ′

′=

′−−=−=

θ

θμμ

Measure of resolution power

Measure of inelasticityMeasure of momentum fraction of struck quark

quark+anti-quarkmom. dists.

gluon mom. dists

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Hadronic tensor:

In full generality,

Quark Green function in background gauge field A of hadron

In the CGC,

Can compute Wμ systematically in expansion about classical field (no OPE!)

McLerran, RV (1999)RV, Acta Phys Polon (1999)Gelis, Peshier

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q

q P

* z

1-z

r

Golec-Biernat-Wusthoff model:

Parameters: Q0 = 1 GeV; = 0.3; x0 = 3* 10-4 ; 0 = 23 mb

Bj, Kogut, SoperNikolaev,ZakharovA. H. Mueller

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Evidence from HERA for geometrical scalingGolec-Biernat, Stasto,Kwiecinski

F2 F2D VM, DVCS = Q2 / QS

2 D V

Marquet, Schoeffel hep-ph/0606079

Scaling confirmed by “Quality factor” analysisGelis et al., hep-ph/0610435

Scaling seen for F2D and VM,DVCS for same QS as F2

Recent NLO BK analysis: Albacete, Kovchegov, hep-ph-0704.0612

x< 0.010 < Q2 < 450 GeV2

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At small x, need to solve JIMWLK/BK equation for energy evolution of

Proper treatment of NLO contributions essentialTriantafyllopolous;Balitsky; Albacete,Gardi,Kovchegov,Weigert,Rummukainen

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II) b-CGC model:

Captures small x BK dynamics (S=0.63 is BK anomalous dimension)

Simple dipole models of small x dynamics

I) IPsat model:

Leading log generalization of Gaussian MV model (logs in x don’t dominate logs in Q2)

QS defined by

Bartels,Golec-Biernat,KowalskiKowalski,Teaney

Iancu,Itakura,MunierKowalski,Motyka,Watt

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Kowalski et al.,hep-ph/0606272

Also see Forshaw et al.hep-ph/0608161

Dipole Models-excellent fits to HERA data

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Typical sat. scale is rather low...QS

2 << 1 GeV2

Caveat: Saturation scale extracted from HERA data inconsistent with model assumptions ?

Model assumes

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Diffractive DIS-smoking gun for saturation

MX

eé

*

P

P P’

15% of all events at HERA are hard diffractive events & diff /tot independent of energy

Naturally explained in dipole saturation models -IPsat and bCGC give good fits (Marquet (2007))

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Strong color fields more accessible in nuclei

Nuclear profile more uniform-study centrality dependence

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Evidence of geometrical scaling in nuclear DISFreund et al., hep-ph/0210139

Nuclear shadowing: Geometrical scaling

Data scale as a function of = Q2 / QS2

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Extension of dipole models to nuclei

Resulting A dependenceof QS

2 ~ A1/3

Kowalski,TeaneyKowalski,Lappi,RV

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Diffractive DIS off nuclei

Very large fraction of e+A events (25-30%) are diffractive -- nucleus either intact (“non breakup”) or breaks up into nucleons separated from the hadronic final state by a large rapidity gap

Kowalski,Lappi,Marquet,RV

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A

Estimates of the saturation scale from RHIC

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Proton-Nucleus collisions in the CGC

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Solve classical Yang-Mills equations:

with two light cone sources

Proton source Nuclear source

Dumitru, McLerran; Blaizot, Gelis, RVGelis, Mehtar-Tani

Obtain kT factorization formula:

Kovchegov, MuellerM. BraunKharzeev,Kovchegov,Tuchin

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Unintegrated distribution:

with the path ordered exponentials in the adjointrepresentation

Compute in CGC EFT

=

Encodes both multiple scattering and shadowing effects

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Dipole models in D+A:

Kharzeev,Kovchegov,TuchinAlbacete,Armesto,Salgado,Kovner,WiedemannBlaizot, Gelis, RV

D-Au pt spectra compared toCGC predictionHayashigaki, Dumitru, Jalilian-Marian

Review: Jalilian-Marian, Kovchegov, hep-ph/0505052

Forward pp @ RHIC as wellBoer, Dumitru, PRD 74, 074018 (2006)

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Extrapolation of BK-fit to RHIC LF data to LHCdn/dy|_{y=0} = 1500-2250 in A+A at LHC

Gelis,Stasto, RV, hep-ph/0605087

Natural explanation for limiting fragmentation + deviations in CGC

Jalilian-Marian

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= …

Pair cross-section:

Amputated time ordered quark propagator in classical background field

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Result not kt factorizable in general -can however be “factorized” into novel multi-parton distributions

These multi-parton distributions can be computed:

a) in closed form in Gaussian (MV) approximation - study multiple scattering effects

b) Quantum evolution of distributions determined by JIMWLK or BK RG eqns. - study shadowing effects as well

Blaizot, Gelis, RV

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Interpretation:

Wilson line correlators - the last appears in pair productiononly

Simplify greatly in large N_c limit x-evolution can be computed with Balitsky-Kovchegov eqn.

Blaizot, Gelis, RV; Tuchin

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Numerical solns. of Yang-Mills eqns. for A+Awith dipole initial conditions (Lappi)

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T.Ullrich-based onKowalski, Lappi, RV ; PRL 100, 022303 (2008)

Quantifying the various regimes

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Open questions

Most estimates are leading order

- is the picture robust at NLO/NLL ?

Balitsky;Albacete,Gardi,Kovchegov,Rummukainen,Weigert

Lack of consistency between dipole models of DIS and hadronic collisions

- need “global fits” of well motivated dipole models Lappi,Marquet,Soyez,RV

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Backup slides

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Universal gluodynamics & energy dependence of QS

A1/3

QS2(b)

€

Y

A

p

Small x QCD RG eqns. predict (fixed b) QS

approaches universal behavior with increasing energy (Y) for all hadrons and nuclei-can the approach to this behavior be tested ?

A.H. Mueller, hep-ph/0301109

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In eA DIS, cleanly access cross-over region from weak field to novel strong field QCD dynamics ?

Weak fieldregime

Q2 >> QS2

Strong fieldregime

Q2 << QS2

Qualitative change in final states: eg.,1/Q6 1/Q2 change in elastic vector meson productionMcDermott,Guzey,Frankfurt,Strikman; Review: Frankfurt, Strikman, Weiss

(Talks by Surrow/Newman)