Mini review on saturation and recent developements Cyrille Marquet Service de Physique Théorique -...
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Transcript of Mini review on saturation and recent developements Cyrille Marquet Service de Physique Théorique -...
Mini review on saturation and recent developements
Cyrille MarquetService de Physique Théorique - CEA/Saclay
ICHEP 2006, Moscow, Russia
• Introduction: the saturation regime of QCDweak coupling regime with high gluon densities
• Success of saturationgeometric scaling at HERAhigh-rapidity suppression at RHIC
• Recent developementsPomeron loopsnew scaling laws in the context of
- deep inelastic scattering- particle production in hadron-hadron collisions
• Conclusions
Contents
Introduction
The hadron wavefunction in QCD
light-cone variables:
x and kT : parton kinematics
P+
gggggqqqqqqgqqq .........hadron
non-perturbative
regime: soft QCD
perturbative regime,
dilute system of partons:
leading-twist approximation
hard QCD
perturbative regime,
dense system of partons:
collective phenomena
the saturation regime of QCD
1, 1, ~hadron xkxkk QCDTQCDTQCDT
The saturation scale1, 1, ~hadron xkxkk QCDTQCDTQCDT
The separation between the dilute and dense regimes
is caracterized by a momentum scale:
the saturation scale Qs(x)
The saturation regime of QCD:the perturbative regime that describes the collective behaviorof quarks and gluons inside a hadron
1~)(Q
, 1T
s
T
QCD
kx
ksaturation regime:
a dense system of partons, responsible forstrong color fields and collective phenomena
1)(Q
, 1 T
s
T
QCD
kx
kleading-twist regime:
a dilute system of partons described withparton distributions, collinear factorization …
Qs(x)
saturationregime
leading-twistregime
BalitskyFadin
KuraevLipatov
Dokshitzer GribovLipatov Altarelli Parisi
When is saturation relevant ?
• deep inelastic scattering at small xBj :
• particle production at forward rapidities y :
In processes that are sensitive to the small-x part of the hadron wavefunction
Q2
22
2
Q
Q
WxBj
W 2
with HERA and RHIC: recent gain of interest for saturation physics
in DIS small x corresponds to high energy
saturation relevant for inclusive,diffractive, exclusive events
h
pT , y
yT epsx 2
yT epsx 1
in particle production, small x correspondsto high energy and forward rapidities
saturation relevant for the production ofjets, pions, heavy flavours, dileptons
The success of saturation
r
Probing the saturation regime
),( YrT
In DIS, the probe is a dipole with a small transverse size r ~ 1/Q
what the dipole sees:
the physics is invariant along anyline parallel to the saturation line
T = 1
T << 1 )(Q),( 22 YrTYrT S
perturbative scales probe small distances inside the hadrons
the dipole scattering amplitude:
Evolution of with rapidity Y: given by(in the leading logarithmic approximation)the B-JIMWLK equations
Balitsky Kovchegov
Balitsky Jalilian-Marian Iancu McLerran Weigert Leonidov Kovner
Simpler version: the BK equation
),( YrT
22 1~Q r
A. Stasto, K. Golec-Biernat and J. Kwiecinski, Phys. Rev. Lett. 86 (2001) 596
The geometric scaling of DIS(x, Q2)
this is seen in the data with 0.3
saturation models
fit well F2 data:
K. Golec-Biernat and M. Wüsthoff, Phys. Rev. D59 (1999) 014017J. Bartels, K. Golec-Biernat and H. Kowalski, Phys. Rev. D66 (2002) 014001E. Iancu, K. Itakura and S. Munier, Phys. Lett. B590 (2004) 199
update
)(Q),( 22 YrTYrT S
C. M. and L. Schoeffel, Phys. Lett. B, in press, hep-ph/0606079
Geometric scaling in diffraction
scaling also for vector meson production :
)(Q),( 22 YrTYrT S
Saturation at HERAsaturation predictions describe accurately a number of observables at HERA
• F2D
• Deeply virtual Compton scattering
• Diffractive vector-meson productiont integrated
t dependence
• F2c
S. Munier, A. Stasto and A. Mueller, Nucl. Phys. B603 (2001) 427H. Kowalski and D. Teaney, Phys. Rev. D68 (2003) 114005H. Kowalski and D. Teaney and G. Watt, hep-ph/0606272
V. Goncalves and M. Machado, Phys. Rev. Lett. 91 (2003) 202002
K. Golec-Biernat and M. Wüsthoff, Phys. Rev. D60 (1999) 114023J. Forshaw, R. Sandapen and G. Shaw, Phys. Lett. B594 (2004) 283
L. Favart and M. Machado, Eur. Phys. J C29 (2003) 365L. Favart and M. Machado, Eur. Phys. J C34 (2004) 429
E. Gotsman, E. Levin, M. Lublinsky, U. Maor and E. Naftali, Acta Phys. Polon. B34 (2003) 3255
Saturation at RHICsaturation predictions describe accurately a number of observables at RHIC
• High-rapidity suppression of the nuclear modification factor in d-Au
D. Kharzeev, Y. Kovchegov and K. Tuchin, Phys. Lett. B599 (2004) 23D. Kharzeev, E. Levin and M. Nardi, Nucl. Phys. A747 (2005) 609A. Dumitru, A. Hayashigaki and J. Jalilian-Marian, Nucl. Phys. A765 (2006) 464
kdddN
kdddN
NR hXpp
hXdA
colldA
2
21
BRAHMS data
see recent review: J. Jalilian-Marian and Y. Kovchegov, Prog. Part. Nucl. Phys. 56 (2006) 104
D. Kharzeev, E. Levin and L. McLerran, Nucl. Phys. A 748 (2005) 627
• Azimuthal correlations
STAR data
suppresion ofback-to-backcorrelations
Recent developements
Beyond the B-JIMWLK equationsA. Mueller and A. Shoshi, Nucl. Phys. B692 (2004) 175E. Iancu, A. Mueller and S. Munier, Phys. Lett. B 606 (2005) 342E. Iancu and D. Triantafyllopoulos, Nucl. Phys. A756 (2005) 419
• Several directions:- high-energy effective action
- generelized dipole model
- reggeon field theoryA. Kovner and M. Lublinsky, hep-ph/0512316A. Kovner and M. Lublinsky, hep-ph/0604085
I. Balistky, Phys. Rev. D72 (2005) 074027 Y. Hatta, E. Iancu, L. McLerran, A. Stasto and D. Triantafyllopoulos, Nucl. Phys. A764 (2006) 423S. Bondarenko and L. Motyka, hep-ph/0605185
A. Kovner and M. Lublinsky, Phys. Rev. D72 (2005) 074023C. M., A. Mueller, A. Shoshi and S. Wong, Nucl. Phys. A762 (2005) 252Y. Hatta, E. Iancu, L. McLerran and A. Stasto, Nucl. Phys. A762 (2005)
272
• Trigerring papers in 2004:
• Then between hep-ph/0501088 and hep-ph/0502243: Pomeron loopsA. Mueller, A. Shoshi and S. Wong, Nucl. Phys. B715 (2005) 440E. Levin and M. Lublinsky, Nucl. Phys. A763 (2005) 172E. Iancu and D. Triantafyllopoulos, Phys. Lett. B610 (2005) 253A. Kovner and M. Lublinsky, Phys. Rev. D71 (2005) 085004A. Kovner and M. Lublinsky, Phys. Rev. Lett. 94 (2005) 181603A. Kovner and M. Lublinsky, JHEP 0503 (2005) 001J.-P. Blaizot, E. Iancu, K. Itakura and D. Triantafyllopoulos, Phys. Lett. B615 (2005) 221E. Levin, Nucl. Phys. A763 (2005) 140
Stochasticity in high energy QCD
: related to the average valueD : dispersion coefficient
E. Iancu, A. Mueller and S. Munier, Phys. Lett. B 606 (2005) 342
Pomeron loops stochasticity in the evolution
similarities between the QCD equation and thes-FKPP equation well-known in statistical physics
(for ) DYSS 22 Q/Qln
C. M., G. Soyez and B.-W. Xiao, Phys. Lett. B, in press, hep-ph/0606233
DYDYP S )Q/Qln²(exp1)Q(ln
22S2
S
the saturation scale is a stochastic variable distributedaccording to a Gaussian probability law:
corrections to the Gaussian law forimprobable fluctuations also known
Y
r
A new scaling law
If DY << 1, the diffusion is negligible and with )(Q),( 22 YrTYrT S
we recover geometric scaling
One obtains the physical dipole amplitude by averaging the event-by-event amplitude which obeys the Langevin equation
we even know the functional form for : DYS 2Qr²ln
DYYrTYrT S )(Qln),( 22
DYYrErfcYrT S )(Qln21),( 22
If DY >> 1, the diffusion is important and
E. Iancu and D. Triantafyllopoulos, Nucl. Phys. A756 (2005) 419C. M., R. Peschanski and G. Soyez, Phys. Rev. D73 (2006) 114005
new regime: diffusive scaling
in the diffusive scaling regime (up to momenta k ~ 1/r much bigger than the saturation scale ):
- cross-sections are dominated by events that feature the hardest fluctuation of the saturation scale - in average the scattering is weak, yet saturation is the relevant physics
New Physics:
),( YrT
Implications for DIS
an intermediate energy regime:geometric scalingHERA
it seems that HERA is probing
the geometric scaling regime
22 1~Q r
Y. Hatta, E. Iancu, C.M., G. Soyez and D. Triantafyllopoulos, Nucl. Phys. A773 (2006) 95
)(Q),( 22 YrTYrT S
In the diffusive scaling regime, saturation is the relevant physics
up to momenta much higher than the saturation scale
at higher energies, a newscaling law: diffusive scaling
within the LHC energy range?
DYYrTYrT S )(Qln),( 22
In the geometric scaling regime
is peaked around k ~ QS(Y) :
In forward particle production, the transverse momentum spectrum is obtained fromthe unintegrated gluon distribution of the small-x hadron
Implications for particle production
),( Yk
Y),( Yk
important in view of the LHC: large pT , small values of x
E. Iancu, C.M. and G. Soyez, hep-ph/0605174
DYk
DYYk S )Q/²ln²(exp1),(
2
In the diffusive scaling regime :
Y
Is diffusive scaling within the LHC energy range?
Hard to tell: theoretically, we have a poor knowledge of the coefficient D
• The saturation regime of QCD:the perturbative regime that describes the small-x part of a hadron wavefunction weak coupling regime with high parton densities
• Sensitivity to the saturation:in deep inelastic scattering at small xBj
in forward particle production in hadron-hadron collisions HERA and RHIC have initiated strong interest this past decadeand saturation has had some success
• Over the past 2 years, new theoretical developements:inclusion of Pomeron loops in the QCD evolution towards high energies several directions for studying the consequences: stochasticity, high-energy effective action, generelized dipole model, reggeon field theory, …for the most part, phenomenology yet to come new scaling laws in the context of DIS and particle production
Conclusions