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)