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Mini review on saturation and recent developements

Mini review on saturation and recent developements. Cyrille Marquet S ervice de Ph ysique T héorique - CEA/ Saclay. ICHEP 2006, Moscow, Russia. Contents. Introduction: the saturation regime of QCD weak coupling regime with high gluon densities

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Mini review on saturation and recent developements

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  1. Mini review on saturation and recent developements Cyrille Marquet Service de Physique Théorique - CEA/Saclay ICHEP 2006, Moscow, Russia

  2. 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

  3. Introduction

  4. 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

  5. saturation 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 scale The separation between the dilute and dense regimes is caracterized by a momentum scale: the saturation scale Qs(x)

  6. 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

  7. The success of saturation

  8. r T = 1 T << 1 the physics is invariant along any line parallel to the saturation line Probing the saturation regime perturbative 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

  9. 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:

  10. Geometric scaling in diffraction  C. M. and L. Schoeffel, Phys. Lett. B, in press, hep-ph/0606079 scaling also for vector meson production :

  11. 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

  12. 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 RHIC saturation 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

  13. Recent developements

  14. 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 equations A. 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:

  15. Y 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 QCD Pomeron 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

  16. 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 law One 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

  17. at higher energies, a new 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 DIS Y. 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

  18. Y 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 production important 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) :

  19. 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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