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Mini review on saturation and recent developements

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### Mini review on saturation and recent developements

Cyrille Marquet

Service de Physique Théorique - CEA/Saclay

ICHEP 2006, Moscow, Russia

Contents

- 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

The hadron wavefunction in QCD

light-cone variables:

P+

x and kT : parton kinematics

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

regime

Qs(x)

leading-twist regime:

a dilute system of partons described with

parton distributions, collinear factorization …

leading-twist

regime

Balitsky

Fadin

Kuraev

Lipatov

saturation regime:

a dense system of partons, responsible for

strong color fields and collective phenomena

Dokshitzer Gribov

Lipatov Altarelli Parisi

The saturation regime of QCD:the perturbative regime that describes the collective behaviorof quarks and gluons inside a hadron

The saturation scaleThe separation between the dilute and dense regimes

is caracterized by a momentum scale:

the saturation scale Qs(x)

When is saturation relevant ?

In processes that are sensitive to the small-x part of the hadron wavefunction

- deep inelastic scattering at small xBj :
- particle production at forward rapidities y :

in DIS small xcorresponds to high energy

Q2

saturation relevant for inclusive,

diffractive, exclusive events

W 2

h

pT , y

in particle production, small xcorresponds

to high energy and forward rapidities

saturation relevant for the production of

jets, pions, heavy flavours, dileptons

with HERA and RHIC: recent gain of interest for saturation physics

T = 1

T << 1

the physics is invariant along any

line parallel to the saturation line

Probing the saturation regimeperturbative scales probe small distances inside the hadrons

In DIS, the probe is a dipole with a small transverse size r ~ 1/Q

the dipole scattering amplitude:

what the dipole sees:

Evolution of with rapidity Y: given by

(in the leading logarithmic approximation)

the B-JIMWLK equations

Balitsky Jalilian-Marian Iancu McLerran Weigert Leonidov Kovner

Simpler version: the BK equation

Balitsky Kovchegov

The geometric scaling of DIS(x, Q2)

this is seen in the data with 0.3

A. Stasto, K. Golec-Biernat and J. Kwiecinski, Phys. Rev. Lett. 86 (2001) 596

update

K. Golec-Biernat and M. Wüsthoff, Phys. Rev. D59 (1999) 014017

J. Bartels, K. Golec-Biernat and H. Kowalski, Phys. Rev. D66 (2002) 014001

E. Iancu, K. Itakura and S. Munier, Phys. Lett. B590 (2004) 199

saturation models

fit well F2 data:

Geometric scaling in diffraction

C. M. and L. Schoeffel, Phys. Lett. B, in press, hep-ph/0606079

scaling also for vector meson production :

Saturation at HERA

saturation predictions describe accurately a number of observables at HERA

- F2D
- Deeply virtual Compton scattering
- Diffractive vector-meson productiont integratedt dependence
- F2c

K. Golec-Biernat and M. Wüsthoff, Phys. Rev. D60 (1999) 114023

J. Forshaw, R. Sandapen and G. Shaw, Phys.Lett. B594 (2004) 283

L. Favart and M. Machado, Eur. Phys. J C29 (2003) 365

L. 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

S. Munier, A. Stasto and A. Mueller, Nucl. Phys. B603 (2001) 427

H. Kowalski and D. Teaney, Phys. Rev. D68 (2003) 114005

H. Kowalski and D. Teaney and G. Watt,hep-ph/0606272

V. Goncalves and M. Machado, Phys. Rev. Lett. 91 (2003) 202002

Azimuthal correlations

suppresion of

back-to-back

correlations

D. Kharzeev, E. Levin and L. McLerran, Nucl. Phys. A 748 (2005) 627

STAR data

Saturation at RHICsaturation predictions describe accurately a number of observables at RHIC

see recent review: J. Jalilian-Marian and Y. Kovchegov, Prog.Part.Nucl.Phys. 56 (2006) 104

High-rapidity suppression of the nuclear modification factor in d-Au

BRAHMS data

D. Kharzeev, Y. Kovchegov and K. Tuchin,Phys. Lett. B599 (2004) 23

D. Kharzeev, E. Levin and M. Nardi,Nucl. Phys. A747 (2005) 609

A. Dumitru, A. Hayashigaki and J. Jalilian-Marian, Nucl.Phys. A765 (2006)464

Then between hep-ph/0501088 and hep-ph/0502243: Pomeron loops

A. Mueller, A. Shoshi and S. Wong, Nucl. Phys. B715 (2005) 440

E. Levin and M. Lublinsky, Nucl.Phys. A763 (2005) 172

E. Iancu and D. Triantafyllopoulos, Phys. Lett. B610 (2005) 253

A. Kovner and M. Lublinsky, Phys.Rev. D71(2005) 085004

A. Kovner and M. Lublinsky, Phys.Rev.Lett. 94 (2005) 181603

A. Kovner and M. Lublinsky, JHEP 0503 (2005) 001

J.-P. Blaizot, E. Iancu, K. Itakura and D. Triantafyllopoulos, Phys. Lett. B615 (2005) 221

E. Levin, Nucl.Phys. A763 (2005) 140

Several directions:- high-energy effective action- generelized dipole model- reggeon field theory

I. Balistky, Phys.Rev. D72 (2005) 074027

Y. Hatta, E. Iancu, L. McLerran, A. Stasto and D. Triantafyllopoulos, Nucl. Phys. A764 (2006) 423

S. Bondarenko and L. Motyka, hep-ph/0605185

A. Kovner and M. Lublinsky, Phys.Rev. D72 (2005) 074023

C. M., A. Mueller, A. Shoshi and S. Wong, Nucl. Phys. A762 (2005) 252

Y. Hatta, E. Iancu, L. McLerran and A. Stasto,Nucl. Phys. A762 (2005) 272

A. Kovner and M. Lublinsky, hep-ph/0512316

A. Kovner and M. Lublinsky, hep-ph/0604085

Beyond the B-JIMWLK equationsA. Mueller and A. Shoshi, Nucl. Phys. B692 (2004) 175

E. Iancu, A. Mueller and S. Munier, Phys. Lett. B 606 (2005) 342

E. Iancu and D. Triantafyllopoulos, Nucl. Phys. A756 (2005) 419

Trigerring papers in 2004:

r

the saturation scale is a stochastic variable distributed

according to a Gaussian probability law:

C. M., G. Soyez and B.-W. Xiao, Phys. Lett. B, in press, hep-ph/0606233

(for )

corrections to the Gaussian law for

improbable fluctuations also known

Stochasticity in high energy QCDPomeron loops stochasticity in the evolution

similarities between the QCD equation and thes-FKPP equation well-known in statistical physics

E. Iancu, A. Mueller and S. Munier, Phys. Lett. B 606 (2005) 342

: related to the average valueD : dispersion coefficient

If DY >> 1, the diffusion is important and

new regime: diffusive scaling

we even know the functional form for :

E. Iancu and D. Triantafyllopoulos, Nucl. Phys. A756 (2005) 419

C. M., R. Peschanski and G. Soyez, Phys. Rev. D73 (2006) 114005

New Physics:

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

A new scaling lawOne obtains the physical dipole amplitude by averaging the event-by-event amplitude which obeys the Langevin equation

If DY << 1, the diffusion is negligible and with

we recover geometric scaling

scaling law: diffusive scaling

within the LHC energy range?

HERA

In the diffusive scaling regime, saturation is the relevant physics

up to momenta much higher than the saturation scale

Implications for DISY. Hatta, E. Iancu, C.M., G. Soyez and D. Triantafyllopoulos, Nucl. Phys. A773 (2006) 95

an intermediate energy regime:

geometric scaling

it seems that HERA is probing

the geometric scaling regime

In the diffusive scaling regime :

E. Iancu, C.M. and G. Soyez, hep-ph/0605174

Y

Is diffusive scalingwithin the LHC energy range?

Hard to tell: theoretically, we have a poor knowledge of the coefficient D

Implications for particle productionimportant in view of the LHC: large pT , small values of x

In forward particle production, the transverse momentum spectrum is obtained from

the unintegrated gluon distribution of the small-x hadron

In the geometric scaling regime

is peaked around k ~ QS(Y) :

Conclusions

- 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

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