Recent progress in the Color Glass Condensate : Recent progress in the Color Glass Condensate Kazunori Itakura
Institute of Particle and Nuclear Studies
KEK Stained glass by M. Chagall (1964) at United Nations in New York
Outline : 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)
Phenomenological applications
DIS at HERA, deuteron-Au collisions at RHIC,
predictions for LHC
Recent Progress in Theory
Physics beyond the BK equation
Summary
Introduction/Motivation : 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 ?
as<<1, 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
Important Experimental Results : Important Experimental Results Deep inelastic scattering (DIS) at HERA
Steep rise of F2 (and gluon density) at small x Q2 = qT2 : transverse resolution
x =p+/P+ : longitudinal mom. fraction 1/Q 1/xP+ g*
Important Experimental Results : Important Experimental Results Hadronic cross section at high energy (total cross sec. for pp) Including cosmic ray data
of AKENO and Fly’s eye
High energy limit of QCD : High energy limit of QCD Keys: many gluons, unitarity, universality Color Glass Condensate (CGC) !! A universal form of matter at high energy Gluons have “color” High density !
occupation number
~ 1/as at saturation created from “frozen” random color source, that evolves slowly compared to natural time scale
The Balitsky-Kovchegov equation : The Balitsky-Kovchegov equation A basic equation for the CGC [Balitsky, Kovchegov, Braun] Derived from QCD by using resummation w.r.t. (as ln s)n & strong gluonic field in the target [Braun,Golec-Biernat,Motyka,Stasto,Marquet,Soyez] [Levin,Tuchin,Iancu,KI,McLerran,Mueller,Triantafyllopoulos,Kozlov] A nonlinear differential equation, solved numerically with/without impact parameter in coordinate/momentum space analytically in some separate kinematical regimes √
Global energy dependence : Global energy dependence Exponential growth is tamed by the nonlinear term saturation !
Initial condition dependence disappears
at late time universal !
Reaction-diffusion dynamics : 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). FKPP = “logistic” + “diffusion” Logistic : “reaction” part, transition
from unstable to stable states
Diffusion : expansion of stable region
Traveling wave solution u=1: stable u=0:unstable *take the 2nd order expansion of the BFKL kernel around its saddle point Well-understood in non-equilibrium statistical physics including directed percolation, pattern formation, spreading of epidemics… t t’ > t
Saturation scale & Geometric scaling : 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.
“Phase diagram” of a proton as seen in DIS : “Phase diagram” of a proton as seen in DIS Non-perturbative (Regge) 1/x
in log scale Q2 in log scale Parton gas Extended
scaling
regime CGC Higher energies Fine transverse resolution BFKL,
BK DGLAP LQCD2 QS2(x) ~ 1/xl: grows as x 0
as(QS2) << 1 weak coupling QS4(x)/LQCD2
Phenomenological applications : Phenomenological applications Deep inelastic scattering at HERA
2. Deuteron-Au collision at RHIC Similarity btw HERA (x~10-4, A=1) and RHIC (x~10-2, A=200)
QS(HERA) ~ QS(RHIC)
Phenomenological applications : 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
DIS at HERA : DIS at HERA The simplest and cleanest process precise information about CGC
No nuclear enhancement need very small x to see CGC DIS at small x : color dipole formalism
intuitively transparent formula for the total cross section and F2
DIS at HERA: the CGC fit : DIS at HERA: the CGC fit Fit performed for the data with
small x and moderate Q2
x < 0.01 & 0.045 < Q2 <45 GeV2
- Based on analytic solutions
to the Balitsky-Kovchegov eq.
Including geometric scaling and
its violation, saturation effects.
Only 3 parameters:
proton radius R, x0 and l
for QS2(x)=(x0/x)l GeV2
Good agreement with the data
x0 = 0.26 x 10-4, l = 0.25
The same fit works well for
vector meson (r, f) production,
diffractive F2, FL
[Forshaw et al, Goncalves, Machado ’04]
[Iancu,KI,Munier ‘04]
DIS at HERA : DIS at HERA The CGC fit still needs to be improved.
DGLAP evolution absent at high Q2 (cf. KKT parameterization)
More accurate behavior in transition regime kT ~ QS
Comparison with the numerical solution
need an extra log dependence (that simulates the absorptive boundary)
(will help to remove oscillatory behavior in the Fourier mode)
-Effects “beyond the Balitsky-Kovchegov equation”
NLO or higher order effects (The BK equation is the LO results)
Effects of fluctuation
-More precise experimental data
especially for FL
……
Deuteron-Au collision at RHIC : Deuteron-Au collision at RHIC Going forward in p(d)-A collision corresponds
to probing nuclear wavefunction at smaller x
Nuclear modification factor (Brahms)
If RdAu=1, d-Au collision is just a summation of pp (up to iso-spin effect) Cronin enhancement at h=0, suppression at h=3.2 d Au q, g g
Deuteron-Au collision at RHIC : Deuteron-Au collision at RHIC Standard approach [Vogt, Guzey-Strikman-Vogelsang, ’04] h X fa fb d Au c a b
Deuteron-Au collision at RHIC : Deuteron-Au collision at RHIC CGC approach 21 process is dominant when the target nucleus is saturated [Kharzeev,Kovchegov,Tuchin, ’04
Dumitru,Hayashigaki,Jalilian-Marian, ’05, etc, etc…..] h Au (CGC) d sdipole fq Dq /h Information of saturation enters through sdipole
“The CGC fit” or “KKT parameterization”
Also important to include DGLAP evolution of deuteron (projectile) Results:
Averaged xAu is small enough ~ 10-3
consistent picture within the CGC framework
Can explain the observed suppression
Deuteron-Au collision at RHIC : Deuteron-Au collision at RHIC Jalilian-Marian ’04
quark production
LO GRV98
for deuteron
+IIM param.
(the CGC fit)
+FF(LOKKP)
+K factor pt spectrum in the CGC approaches Dumitru-Hayashigaki-
Jalilian-Marian ’05
Quark + gluon production
DGLAP for deuteron
+ FF(LO KPP)
+ LO CTEQ5 with K factor
+ KKT param.
Kharzeev-Kovchegov-Tuchin ’04
quark+gluon production
Valence quark
distribution
+ KKT param.
+ FF(LOKKP)
+nonpert. Cronin x- and DGLAP evolution
Deuteron-Au collision at RHIC : Deuteron-Au collision at RHIC [Albacete,Armesto,Kovner,Salgado,Wiedemann,Gelis,Jalilian-Marian,Kharzeev,Kovchegov,Tuchin, Accardi,Gyulassy,Levin,McLerran,Iancu,KI,Triantafyllopoulos,Venugopalan] 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 Lots of studies in the CGC framework (see a review by Kovchegov & Jalilian-Marian) Running coupling effects evaluated [Iancu,KI,Triantafyllopoulos]
Various observables show “suppression” due to saturation.
EM probes: dileptons, photons [Jalilian-Marian,Baier,Mueller,Shiff,Gay-Ducati,Betemps]
qqbar (meson) production [Blaizot,Fujii,Gelis,Venugopalan,Kharzeev,Tuchin]
Jet azimuthal correlations disappear due to “mono-jet” production.
[Kharzeev,Levin,McLerran,Baier,Kovner,Nardi,Wiedemann]
Still need to understand identified particle dependence
CGC + recombination??
Need to treat BOTH 22 and 21 processes at the same time….
Phase diagram with numbers : Phase diagram with numbers 10-4 10-2 From the CGC fit
Qs2(x)~(10-4/x)0.25 100 x in log Q2 in log 103 CGC Extended
Scaling
~BFKL Parton gas HERA proton
CGC at LHC : CGC at LHC LHC √sNN = 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
Recent progress in theory Beyond the BK equation : Recent progress in theory Beyond the BK equation
Beyond the BK equation : 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 PPP
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” PPP .
This allows one to have Pomeron loops.
Beyond the BK equation : 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
The high energy asymptotics of scattering processes in QCD
Enberg, Golec-Biernat, Munier, hep-ph/0505101
On the Projectile-Target Duality of the Color Glass Condensate in the Dipole Picture
Marquet, Mueller, Shoshi, Wong, hep-ph/0505229
Fluctuations effects in high-energy evolution of QCD, Soyez, hep-ph/0504129.
Perturbative Odderon in the Dipole Model, Kovchegov, Szymanowski, Wallon, Phys. Lett. B586 (2004) 267
Odderon in the Color Glass Condensate, Hatta, Iancu, Itakura, McLerran, hep-ph/0501171
A classical Odderon in QCD at high energies, Jeon and Venugopalan, Phys. Rev. D71 (2005) 125003 Keep an eye on this subject !!
Summary : 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.
Thanks to : 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 !!
Backup slides : Backup slides
Pomeron Loops : 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 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 Need to supply “Pomeron splitting”
to obtain a Lorentz inv. description !
Odderon : 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 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. [Kovchegov,Szymanovsky,Wallon,Hatta,Iancu,KI,McLerran,Jeon,Venugopalan] A big step towards the description of n-reggeized gluon exchange !!
Geometric scaling : Geometric scaling Geometric scaling approximately exists even outside of CGC!!
“Scaling window” The saturation scale from the data is
consistent with the theoretical results Observed in HERA DIS at small x and moderate Q2
[Stasto,Kwiecinski,Golec-Biernat] CGC Extended
Scaling
regime
Geometric scaling with fluctuation : Geometric scaling with fluctuation Inclusion of Pomeron loops
Stochastic FKPP equation [Iancu, Mueller, Munier] Numerical analysis
by R.Enberg et al.
Geometric scaling is
still valid for not so small x Geometric scaling is strongly violated by the “fluctuation”
More about deuteron-Au @ RHIC : More about deuteron-Au @ RHIC Jalilian-Marian
quark production
LO GRV98
for deuteron
+IIM param.
(the CGC fit)
+FF(LOKKP)
+K factor pt spectrum in the CGC Dumitru-Hayashigaki-
Jalilian-Marian
Quark + gluon production
DGLAP for deuteron
+ FF(LO KPP)
+ LO CTEQ5 with K factor
+ KKT param.
Kharzeev-Kovchegov-Tuchin
quark+gluon production
Valence quark
distribution
+ KKT param.
+ FF(LO,KKP)
+nonpert.Cronin x- and DGLAP evolution