Strong gluon fields in nucleons

1
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
Gribov,Levin,Ryskin Mueller,Qiu
Large x - bremsstrahlung linear evolution
(DGLAP/BFKL)
p, A
Saturation scale QS(x) - dynamical scale below
which non-linear (higher twist) QCD dynamics is
dominant
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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
  non-linear regime
• Renormalization group equations (JIMWLK/BK)
• describe how the QCD dynamics changes with
  energy
• A universal saturation scale QS arises
  naturally in the theory

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Saturation scale grows with energy
Typical gluon kT in hadron/nuclear wave function

• Bulk of high energy cross-sections
• obey dynamics of novel non-linear
• QCD regime
• b) Can be computed systematically in
• weak coupling

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Nuclear OomphSaturation scale grows with A
High energy compact (1/Q lt 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
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Nuclear oomph (II) Diffractive DIS
Kowalski,Lappi,Marquet,RV (2008)
Very large fraction of eA 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
for glue
?S(QS2) ltlt 1
T. Ullrich

• Note Strong constraints from RHIC AA Nch QS2
  and
• ET QS3 - day 1 AA at LHC will provide
  important confirmation
• Careful analysis gives values consistent with
  above
• plot to 15

T. Lappi, arXiv07113039 hep-ph
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Road map of the strong interactions

• 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
Ludlam, McLerran, Physics Today (2003)
Glasma (\Glahs-maa\) Noun non-equilibrium
matter between Color Glass Condensate (CGC)
Quark Gluon Plasma (QGP)
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Little Bang
Big Bang
Hot Era
WMAP data (3x105 years)
QGP
Inflation
CGC/ Glasma
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,RV arXiv0804.2630 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
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From Glasma to Plasma

• NLO factorization formula

• With spectrum, can compute T?? - and match to
• hydro/kinetic theory

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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
STAR preliminary
STAR preliminary
inclusive
inclusive
pt,assoc,cut
pt,assoc,cut
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Evolution of mini-jet with centrality
Same-side peak
Binary scaling reference followed until sharp
transition at ? 2.5 30 of the hadrons in
central AuAu participate in the same-side
correlation
M. Daugherty Session IX, QM2008
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Update the ridge comes into its own
PHENIX sees a ridge

• PHOBOS the ridge extends to very high rapidity

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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
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An example of a small fluctuation spectrum
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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 lt 1/?QCD
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2 particle correlations in the Glasma (I)
Dumitru, Gelis ,McLerran, RV, arXiv0804.3858hep-
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)
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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
Voloshin, Shuryak Gavin, 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 matter
• 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 ??

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P and CP violation in the Glasma
Kharzeev Kharzeev, McLerran, Warringa
Lagrangean invariant under scale (dilatations)
and chiral
transformations for massless quarks
Right
Left
)
(
Both symmetries broken by quantum effects -
anomalies
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QCD vacuum and sphaleron transitions
Vacua labeled by different Chern-Simons ?
E?B
Over the barrier sphaleron transitions can
change the topological charge in an event gt 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)
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Real time Chern-Simons diffusion
At finite T
In the Glasma
Arnold, Moore, PRD73 (2006)
Kharzeev, Krasnitz, RV, Phys. Lett. B545 (2002)
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The Chiral Magnetic effect in the Glasma
Kharzeev,McLerran,Warringa, 0711.0950
Heavy Ion Collisions at RHIC Largest
Terrestrial magnetic fields!
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Magnetic fields Sphaleron transitions Chiral
Magnetism
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
S.Voloshin, hep-ph/0406311
Preliminary STAR result
S. Voloshin et al STAR Coll., QM08
I. Selyuzhenkov et al., STAR Coll.,
nucl-ex/0510069
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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
fits Centrality dependence of QS a la
Kharzeev-Nardi