Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.
-
Upload
theresa-stafford -
Category
Documents
-
view
220 -
download
3
Transcript of Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.
![Page 1: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/1.jpg)
Overview of saturation
Yoshitaka Hatta
(Saclay)
Low-x meeting, 2007, Helsinki
![Page 2: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/2.jpg)
Outline
BFKL and beyond Saturation momentum The BK-JIMWLK equation Fluctuations & Correlations
![Page 3: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/3.jpg)
Regge limit of QCD
E
E
,...,,2 TpMtEs
One of the most challenging problems in QCD is the understanding of its high energy limit.
Can we compute hadron-hadron (nucleus) cross sections in this regime from first principles?
![Page 4: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/4.jpg)
Deep Inelastic Scattering
2Q
xY
1ln
DGLAP
BF
KL
p
222
22
2 QMM
Q
qP
Qx
pX
X
s
Q2
)1( x
![Page 5: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/5.jpg)
The BFKL Pomeron
1x2x
nx
x
p
n
s
x
xn
n
x
ns xnx
dx
x
dx n
1ln
!
111
1
1
ss sxptot
2ln42ln4*
…
xxx n 11
Rapidity ordering
Balitsky, Fadin, Kuraev, Lipatov, `75~`78
![Page 6: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/6.jpg)
Ways to go — beyond BFKL
LLA BFKL predicts indefinite growth of the gluon number.
Infrared diffusion invalidates perturbative treatment in the middle of the ladder.
Many reggeized gluon exchange à la BKP
Next to leading-log approximation (NLLA) Nonlinear equations from gluon saturation
Must be tamed (How?)
![Page 7: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/7.jpg)
12 3
N 4……
High energy QCD as an integrable modelLipatov, `93 Faddeev & Korchemsky, `94
The BKP Hamiltonian is identical to that of an exactly solvable system.Eigenvalue (energy dependence ) obtained by the Bethe ansatz
HHHBKP
s
Heisenberg spin chain0s
1
23
4N
…..
BKP equation at large Nc
![Page 8: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/8.jpg)
Ways to go — beyond BFKL
LLA BFKL predicts indefinite growth of the gluon number.
Infrared diffusion invalidates perturbative treatment in the middle of the ladder.
Many reggeized gluon exchange à la BKP
Next to leading-log approximation (NLLA) Nonlinear equations from gluon saturation
Must be tamed (How?)
![Page 9: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/9.jpg)
Saturation criterion : hadron
)(22 xQQ s
hR
222
),( hs RQxxG
Q
Collinear or kt factorization : One parton from each hadron scatters. Partons inside a hadron do not interact. exponential growth in number
recombinationcross section
# of gluonscomputed in BFKL
When gluons begin to overlap…
![Page 10: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/10.jpg)
A large nucleus ( ) is a dense system from the beginning.
Saturation criterion : nucleus
3/12 AQs
AR22
2),( A
s RQxAxGQ
# of gluons computed in lowest order perturbation theory
At the same time, multiple scattering becomes unsuppressed. (Glauber—Mueller)
A
McLerran & Venugopalan `94
3/1A
![Page 11: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/11.jpg)
The saturation momentum at LLA
Find the line of constant amplitude in the BFKL solution.
Gribov, Levin, Ryskin, `83
21 1
)(
37.0
22 ),( QQxxG
}ln)1()(exp{ 22 QYd
increase with decrease with 2QY
YQCDs
seYQ 9.422 )(
Calculations at (improved) NLO available Triantafyllopoulos `03 Khoze et al. `04
YQCDe 8.92
(fixed coupling)
(running coupling)
![Page 12: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/12.jpg)
The new phase of QCD
2Q
sY ln
DGLAP
BF
KL
)(2 YQs
extended scaling region
![Page 13: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/13.jpg)
Evolution in the presence of saturation
A
dressed propagator
Incoming hadrons (nuclei) are replaced by non-Abelian Weizsacker-Williams fields of strength ~ g1
A
gA gANeed to sum all orders in , or , or both in a single step of evolution
![Page 14: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/14.jpg)
BK-JIMWLK (1996~2001)
BFKL (1975~78)
A
A
Pomeron loop (~20XX)
The long and winding road to unitarity…
A
A
A
A
A
A
BKP (1978~80)
A
A
NLO BFKL (1996~98)
NLO BK(Coming soon !)
![Page 15: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/15.jpg)
The BK-JIMWLK equation
xy
xxA
Yyxc
Y VVN
yxT ][Tr1
1),(
22
22
)()(
)(
2),(
yzzx
yxzdyxT
Ys
Y
YyzTzxTyxTyzTzxT }),(),(),(),(),({
Dipole-nucleus scattering (subprocess of DIS)
BFKL gluon recombination
),(),(),(),( yzTzxTyzTzxT `Mean field’ approximation
)},(exp{
xxAdxigPVx
![Page 16: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/16.jpg)
1
)(rTY
2
1ln
r122 ))(( YQr s
Y`front’
|| yxr : dipole size
The geometric scaling
Mapping onto the traveling wave solution of the FKPP equation
22 ffff xt Munier & Peschanski, `03
Some indication in the HERA data Stasto, Golec-Biernat & Kwiecinski, `01 Marquet & Schoeffel, `06 (diffraction)
Iancu, Itakura & McLerran, `02The scaling persists even when 22sQQ
![Page 17: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/17.jpg)
Application to other processes
Diffractive DIS
pA (and AA) collisions at RHIC
Odderon
The BLV solution : constant in energy Saturation effects tend to suppress the odderon amplitude.
Saturation prediction 2ln1 Qtotdiff Independent of ! x
Saturation models confront RHIC data, doing well.
Multiplicity, pt distribution, heavy quark, , limiting fragmentation, etc. pAR
Inclusive & exclusive Talk by Marquet
![Page 18: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/18.jpg)
Beyond BK—JIMWLK
What’s missing in the BK-JIMWLK?
A kind of mean field approximation, neglecting fluctuations and correlationsin the target wavefunction.
)1(),(),(),(),( 2cNOwzTyxTwzTyxT
xy
zw
Not symmetric w.r.t. the target and projectile,Saturation effect of the projectile missing.
A
A
![Page 19: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/19.jpg)
The gluon number fluctuation
boost
Salam, `96
QCD dipole model
xzy large Nc
Significant consequences in the approach to unitarity.Deep connection to the stochastic FKPP equation in statistical physics.
zdYdyzzx
yxdP s
222
2
)()(
)(
fffff xt22
![Page 20: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/20.jpg)
Universal behavior of the sFKPP equation
1
),( YrT
21ln r
Front position (saturation scale ) becomes a random variable2sQ
Each event shows geometric scaling, but the average does not !
Observed amplitude is obtained after averaging over events.
Y
Iancu, Mueller, Munier, `04
TTTT Factorization `maximally’ violated
![Page 21: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/21.jpg)
Caveats: Requires enormous energy for the fluctuation to become significant. Running coupling may be (very) important.
Talks by Beuf, Kozlov, Soyez
HERA ?
LHC, cosmic ray ??
Updating the phase diagram
Figure from Iancu, Marquet, Soyez `06
![Page 22: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/22.jpg)
ax
bx
abx
Power—law correlation in the transverse plane
01x
Y.H. & Mueller, `07
Small-x gluons are correlated because they come from a common ancestor.
L
abxncorrelatio
1)(zdYd
yzzx
yxdP s
222
2
)()(
)(
![Page 23: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/23.jpg)
Determination of the power
Breakdown of factorizationfrom BFKL. Explicit !
)2(2 0
1)()()()(
abbaba x
xTxTxTxT
ax
bx
abx
Peschanski, `97 Braun & Vacca, `97
Dipole pair density
![Page 24: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/24.jpg)
Quest for unitarity : a difficult but fascinating problem
Continual efforts & progresses, still many open questions
BK-JIMWLK equation : the best ‘simple’ equation including nonlinear effects.
Beyond the BK-JIMWLK : Pomeron loops.
Hadron wavefunction teems with correlations and fluctuations.
Summary
![Page 25: Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649f425503460f94c6162d/html5/thumbnails/25.jpg)
Important theoretical problems
Full inclusion of Pomeron loops, and its physical consequences.
Gluon production in AA collision, quantum evolution.
NLO BK phenomenology
Gelis, Lappi, Venugopalan `07
Talk by Y.H.
Saturation in AdS/CFT ?
Balitsky `06, Kovchegov, Weigert `06, Balitsky, Chirilli, to appear
Talks by Levin and Lublinsky