Recent results on saturation and CGC

1
Recent results on saturation and CGC

• Kazunori Itakura
• Theory Group, KEK
• JAPAN

Stained glass by M. Chagall (1964) at United
Nations in New York
2
Outline

• Introduction/Motivation
• Basic questions, Important experimental
  results
• High energy limit of QCD
• Color Glass Condensate
• The Balitsky-Kovchegov Equation
• A fresh look at the equation from the
  statistical physics
• (The Logistic equation and the FKPP
  equation)
• Recent Progress in Phenomenology
• Deuteron-Au collisions at RHIC,
  predictions for LHC
• Recent Progress in Theory
• Beyond the BK equation
• Summary

3
Introduction/Motivation

• Basic questions/problems which we want to
  answer/understand
• What is the high energy limit of QCD ?
• If it indeed exists,
• - Is it different from the ordinary picture of
  hadrons ?
• - Is it already seen in experiments ?
• - What is the evidence for it ?
• - Can we treat it in weak-coupling techniques ?
• asltlt1, in scatt. with high Q2, or at
  high temperature/density
• What is the information of nucleons relevant for
• high energy scattering ?
• instead of static information such as
  mass, radius at rest, etc

4
Important Experimental Results

• Deep inelastic scattering (DIS) at HERA
• ? Steep rise of F2 (and gluon density) at
  small x

g
1/Q
1/xP
Q2 qT2 transverse resolution x p/P
longitudinal mom. fraction
High density gluons appear at small x high
energy scatt.
5
Important Experimental Results
Hadronic cross section at high energy (total
cross sec. for pp)
Including cosmic ray data of AKENO and Flys eye
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High energy limit of QCD
Keys many gluons, unitarity, universality
A universal form of matter at high energy
? Color Glass Condensate (CGC) !!
High density ! occupation number 1/as at
saturation
created from frozen random color source, that
evolves slowly compared to natural time scale
Gluons have color
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The Balitsky-Kovchegov equation
A basic equation for the CGC
Balitsky, Kovchegov, Braun
v
Derived from QCD by using
resummation w.r.t. (as ln s)n strong
gluonic field in the target
A nonlinear differential equation, solved
numerically with/without impact parameter
in coordinate/momentum space
Braun,Golec-Biernat,Motyka,Stasto,Marquet,Soyez
analytically in some separate kinematical
regimes
Levin,Tuchin,Iancu,KI,McLerran,Mueller,Trianta
fyllopoulos,Kozlov
8
Global energy dependence
Exponential growth is tamed by the nonlinear term
? saturation ! Initial condition dependence
disappears at late time ? universal !

9
Reaction-diffusion dynamics
Munier Peschanski (2003)
With a reasonable approximation, the BK equation
in momentum space is rewritten as the FKPP
equation (Fisher, Kolmogorov, Petrovsky,
Piscounov) where t Y, x ln k2 and
u(t, x) NY(k).
Well-understood in non-equilibrium statistical
physics including directed percolation, pattern
formation, spreading of epidemics
FKPP logistic diffusion
u1 stable
Logistic reaction part, transition
from unstable to stable states
Diffusion expansion of stable region ?
Traveling wave solution
t
t gt t
u0unstable
take the 2nd order expansion of the BFKL kernel
around its saddle point
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Saturation scale Geometric scaling
Fact 1 For a traveling wave solution, one
can define the position of a wave
front x(t) v(t)t .
Fact 2 At late time, the shape of a traveling
wave is preserved, and the solution is only
a function of x vt.
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Phase diagram of a proton as seen in DIS
QS2(x) 1/xl grows as x ? 0 as(QS2) ltlt 1
weak coupling
CGC
Extended scaling regime
QS4(x)/LQCD2
Higher energies ?
BFKL, BK
Non-perturbative (Regge)
1/x in log scale
Parton gas
DGLAP
Q2 in log scale
Fine transverse resolution ?
LQCD2
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Recent progress in phenomenology
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Phenomenological applications

• DIS at HERA
• Au-Au at RHIC
• Deuteron-Au at RHIC
• p-Pb and Pb-Pb at LHC (predictions)
• High Energy Cosmic Rays

14
Deuteron-Au at RHIC

• Going forward in p(d)-A collision corresponds to
  probing nuclear wavefunction at smaller x
• Nuclear modification factor (Brahms)
• 
  If RdAu1, d-Au is just
• 
  a summation of pp
• 
  (up to iso-spin effect)

d
q, g
g
Au
Cronin enhancement at h0, suppression at h3.2
Lots of studies in the CGC framework (see a
review by Kovchegov Jalilian-Marian)

• Qualitative behaviors consistent with
  predictions of CGC.
• Cronin peak ? multiple Glauber-Mueller
  scattering (McL.-V. model)
• High pt suppression ? due to mismatch between
  evolution speeds
• of proton nucleus. Nucleus
  grows only slowly due to saturation.
• Quantitative results also available

Albacete,Armesto,Kovner,Salgado,Wiedemann,Gelis,J
alilian-Marian,Kharzeev,Kovchegov,Tuchin,
Accardi,Gyulassy,Levin,McLerran,Iancu,KI,Triantafy
llopoulos,Venugopalan
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Deuteron-Au at RHIC

• Running coupling effects evaluated
  Iancu,KI,Triantafyllopoulos
• DGLAP improvements on the projectile side
  (deuteron) necessary
• Averaged x2 in 2?1 kinematics is 10-3
  for RHIC y3 (private communication)
• 
  Dumitru,Hayashigaki,Jalilian-Marian ? see talk
  by Jalilian-Marian

• Various observables show suppression due to
  saturation.
• EM probes dileptons, photonsJalilian-Mari
  an,Baier,Mueller,Shiff,Gay-Ducati,Betemps
  
• qqbar (meson) production
  Blaizot,Fujii,Gelis,Venugopalan,Kharzeev,Tuchin
• 
  ? see talks by Fujii Lappi
• Jet azimuthal correlations disappear due
  to mono-jet production.
• 
  Kharzeev,Levin,McLerran,Baier,Kovner,Nar
  di,Wiedemann

• Other approaches.
• Standard nuclear shadowing (NLO Leading Twist)
  with 2?2 process
• 
  
  Vogt,Guzey,Strikman,Vogelsang
• Parton recombination ? identified particle
  dependence Hwa,Yang,Fries
• Re-scattering effects with factorization
  formalism of pQCD Qiu,Vitev

? Need more detailed investigation to be
convinced
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Phase diagram with numbers
From the CGC fit Qs2(x)(10-4/x)0.25
proton
x in log
Extended Scaling BFKL
CGC
10-4
Parton gas
HERA
10-2
100
103
Q2 in log
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CGC at LHC
LHC vsNN 14 TeV for pp, 5.5 TeV for
PbPb For the same pt, Qs2(LHC) is increased by
a factor of 3 than Qs2 (RHIC). Qs2(LHC) 3 --
10 GeV2 Number of gluons in the saturation
regime increases. ?
Effects of saturation will be more visible!!
mid forward
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Recent progress in theoryBeyond the BK equation
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Beyond the BK equation

• The complete picture of high energy scattering in
  QCD will contain
• Pomeron 2 gluon exchange, C-even state
• Odderon 3 gluon exchange, C-odd state
• Reggeon quark-antiquark exchange,..
• and interaction among them

The BK equation -- multiple exchange of P, and
P-merging PP?P ? Need to go beyond the
BK equation !!
In order to correctly describe the interaction
among them, one needs to modify JIMWLK
Hamiltonian so that it contains P-splitting
P?PP . This allows one to have Pomeron loops.
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Beyond the BK equation

• Small-x physics beyond the Kovchegov equation,
  Mueller and Shoshi, Nucl.Phys. B692 (2004)
  175-208
• Universal behavior of QCD amplitudes at high
  energy from general tools of statistical physics,
  
• Iancu, Mueller, and Munier, Phys. Lett.
  B606 (2005) 342-350
• A Langevin equation for high energy evolution
  with pomeron loops,
• Iancu and Triantafyllopoulos, Nucl.Phys.
  A756 (2005) 419-467
• Extension of the JIMWLK Equation in the Low Gluon
  Density Region
• Mueller, Shoshi and Wong, Nucl.Phys. B715
  (2005) 440-460
• Non-linear QCD evolution with improved
  triple-pomeron vertices
• Iancu and Triantafyllopoulos, Phys.Lett.
  B610 (2005) 253-261
• In pursuit of Pomeron loops the JIMWLK equation
  and the Wess-Zumino term
• Kovner and Lublinsky, Phys.Rev. D71 (2005)
  085004
• From target to projectile and back again
  selfduality of high energy evolution
• Kovner and Lublinsky, Phys.Rev.Lett. 94
  (2005) 181603
• Duality and Pomeron effective theory for QCD at
  high energy and large Nc
• Blaizot, Iancu, Itakura,
  Triantafyllopoulos, Phys.Lett. B615 (2005)
  221-230
• High energy amplitude in the dipole approach with
  Pomeron loops asymptotic solution
• Levin, hep-ph/0502243
• Effective Hamiltonian for QCD evolution at high
  energy
• Hatta, Iancu, McLerran, Stasto,
  Triantafyllopoulos, hep-ph/0504182, see also
  hep-ph/0505235

Keep an eye on this subject !!
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Summary

• High enegy limit of QCD is the Color Glass
  Condensate
• - high density gluonic matter which shows
• ? saturation of gluon distribution
  (non-linearity),
• ? unitarization of scattering amplitude,
• ? universal (insensitive to initial
  conditions)
• ? provides natural interpretation of
  geometric scaling
• All of these are confirmed by the close analogy
  with
• the FKPP equation for
  reaction-diffusion dynamics.
• CGC can be compared with experiments
• ? small x data in DIS at HERA
• ? suppression of RpA in deuteron-Au at
  forward rapidity
• Theoretical framework under re-construction
• new direction BEYOND the BK equation
• We are now approaching the complete description
  of high energy scattering in QCD.

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Thanks to

• My collaborators (chronological)
• Larry McLerran, Edmond Iancu, Elena
  Ferreiro,
• Yuri Kovchegov, Derek Teaney, Stephen
  Munier,
• Dionysis Triantafyllopoulos, Yoshitaka
  Hatta,
• Jean-Paul Blaizot
• My colleagues (possible future collaborators,
  alphabetical)
• Adrian Dumitru, Rikard Enberg, Hiro
  Fujii,
• Francois Gelis, Arata Hayashigaki,
  Tetsu Hirano,
• Jamal Jalilian-Marian, Dmitri Kharzeev,
  Cyrille Marquet,
• Al Mueller, Yasushi Nara, Robi
  Peschanski,
• Gregory Soyez, Kirill Tuchin, Raju
  Venugopalan,
• and all the people who are interested in
  CGG !!

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Backup slides
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Pomeron Loops

• Necessary ingredient for the complete description
  of the high energy limit of QCD
• The BK equation describes
• multiple exchange of BFKL Pomerons and
  fan diagrams (merging)

BUT, not the opposite Pomeron splitting
diagrams ? asymmetric under the
exchange btw projectile and target
Need to supply Pomeron splitting to obtain a
Lorentz inv. description !

• a new concept duality btw proj. target ?
  related to fluctuation (BK is the mean field
  approximation)
• Modification to BK (and JIMWLK) done ?
  stochastic FKPP equation

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Odderon

• The BK eq. is for the hard Pomeron two
  reggeized gluon exchange
• 
  even under the charge
  conjugation.

Perturbative QCD ? hard Odderon 3 reggeized
gluon exchange in C-odd state, obeys the BKP
equation Bartels,
Kwiecinski-Praszalowicz Recent progress
New description of Odderon in CGC
Kovchegov,Szymanovsky,Wallon,Hatta,Iancu,KI,McLer
ran,Jeon,Venugopalan

• Can define relevant C-odd operators for
  dipole-CGC 3quark-CGC scatt.
• Reproduce the BKP equation in the linear regime
• In the dipole-CGC scattering, nonlinear effects
  kills the Odderon.

A big step towards the description of n-reggeized
gluon exchange !!
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Geometric scaling
Observed in HERA DIS at small x and moderate Q2

Stasto,Kwiecinski,Go
lec-Biernat
The saturation scale from the data is consistent
with the theoretical results
Extended Scaling regime
CGC
Geometric scaling approximately exists even
outside of CGC!! ? Scaling window
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Geometric scaling with fluctuation
Inclusion of Pomeron loops ?
Stochastic FKPP equation Iancu, Mueller, Munier
Geometric scaling is strongly violated by the
fluctuation

• Numerical analysis
• by R.Enberg et al.
• Geometric scaling is
• still valid for not so small x

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More about deuteron-Au _at_ RHIC
pt spectrum in the CGC
Jalilian-Marian quark production LO GRV98 for
deuteron IIM param. (the CGC
fit) FF(LOKKP) K factor
Kharzeev-Kovchegov-Tuchin quarkgluon
production Valence quark distribution KKT
param. FF(LO,KKP) nonpert.Cronin
Dumitru-Hayashigaki- Jalilian-Marian Quark
gluon production DGLAP for deuteron FF(LO
KPP) LO CTEQ5 with K factor KKT param.
x- and DGLAP evolution