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Particule production and saturation Cyrille Marquet SPhT, Saclay ISMD 2005, Kromeriz, Czech Republic

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Introduction Bjorken limit and Regge limit of perturbative QCD High-energy QCD (the Regge limit) and saturation scattering matrix for high-energy partons qq dipoles, gg dipoles, multipoles, … observables at small-x HERA Phenomenology forward jets vector mesons, DVCS diffractive jets Conclusion and outlook Contents

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Introduction

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The Bjorken limit of pQCD Consider a collision of hadronic particules with a center- of-mass energy W and a hard scale Q >> QCD The Bjorken limit: Q² , W² with Q²/W² fixed ( x Bj in DIS) Operator product expansion At leading twist: collinear factorization gluon distribution DGLAP evolution Higher twists suppressed by powers of Q² Scattering amplitudes decrease with increasing Q² Transverse view of the proton in DIS

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The Regge limit of pQCD The Regge limit: W² with Q² fixed (x Bj 0 in DIS) One has to introduce a new scale: the saturation scale Q sat (W²) Consider a collision of hadronic particules with a center- of-mass energy W and a hard scale Q >> QCD If W is such that Q sat (W²) < Q, no higher-twist effects k T -factorization, unintegrated gluon distribution, BFKL evolution scattering amplitudes increase with increasing W If W is such that Q sat (W²) > Q, density effects are important (higher-twist) need to go beyond the OPE, strong gluon fields, CGC, saturation … scattering amplitudes approach unitarity limit Q sat (W²)

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High-energy QCD (the Regge limit)

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For an incoming quark of color i, at transverse position x: The action of the S matrix is Scattering matrix for high-energy partons For a gluon: the same with the adjoint Wilson line W A Wilson lines W F and W A : the degrees of freedom of high-energy QCD Y = log(W²) : total rapidity

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T qq (x, x’,Y): the scattering amplitude of a qq dipole off the target: T qq (x, x’; y, y’,Y): the scattering amplitude of two qq dipoles: T gg (x, x’,Y): the scattering amplitude of a gg dipole: and more generally any multipole Dipoles and multipoles (2) Instead of directly the Wilson lines, colorless combinations arise as the degrees of freedom: We have denoted

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Simplest illustration : DIS r: transverse size of the dipole b: impact parameter z: longitudinal momentum fraction of the quark does not depend on z in the high-energy limit the qq dipole amplitude T qq (r, b, Y) appears Y: total rapidity

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Observables at small-x Particule production phenomenology: jet cross-sections, heavy-quark production, diffractive vector mesons production, di-lepton production, multiplicities … have been studied in this high-energy QCD framework The same dipole amplitudes enter in the formulation of inclusive, diffractive, exclusive cross-sections Y [A], and therefore T qq, T gg, T qqg … are mainly non-perturbative, however the Y evolution is computable (in the leading logarithmic approximation) for more on these equations, see Larry McLerran’s talk tomorrow and Robi Peschanski’s talk sunday More generally, any cross-section is a function of T qq, T gg, T qqg … The more exclusive the final state is, the more complicated the corresponding multipoles are How does one compute T qq, T gg, T qqg …? With

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HERA phenomenology for particule production * -proton collisions

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Forward-jet production proton + * forward-jet + X photon virtuality: Q jet transverse momentum: k with Q k » QCD and x Bj <<1, small-x effets expected photon qq dipole and jet emission gg dipole C.M., R. Peschanski and C. Royon, Phys. Lett. B 599 (2004) 236 C.M. and C. Royon, in preparation the different observables are well described by BFKL and saturation models NLOQCD is a factor 2 below the data at small-x data: see Leif Joensson’s talk later today

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Diffractive vector-meson production S. Munier, A. Stasto and A. Mueller, Nucl. Phys. B 603 (2001) 427 t = -q² the S-matrix is extracted from the data for S(1/r 1Gev, b 0, x 5.10 -4 ) 0.6 HERA is entering the saturation regime or need a parametrization for

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Diffractive J-Psi production (1) H. Kowalski and D. Teaney, Phys. Rev. D 68 (2003) 114005 dipole amplitude: ansatz for the b dependence Y = log(1/x)

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Diffractive J-Psi production (2) E. Gotsman, E. Levin, M. Lublinsky, U. Maor and E. Naftali, Acta Phys. Polon. B34 (2003) 3255 dipole amplitude obtained from a numerical solution of the BK equation ansatz for the b dependence in the initial condition

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Deeply Virtual Compton Scattering they compute they assume L. Favart and M. Machado, Eur. Phys. J C29 (2003) 365 Eur. Phys. J C34 (2004) 429 Bartels Golec-biernat Kowalski model to do better and compute, one needs a model for need an analysis of the BK equation at non zero momentum transfer: with t = -q² C.M. and G. Soyez, Nucl. Phys. A, in press C.M., R. Peschanski and G. Soyez, Nucl. Phys. A 756 (2005) 399 Y = log(1/x)

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Diffractive photon dissociation is the dominant contribution to the diffractive cross-section diff at large M X in DIS: elas : involves the qq dipole fluctuation, dominant for small-mass final states dissoc : involves higher Fock state fluctuations: qqg, …dominant for large- mass final states Diffractive jet production (1) = Q²/M X ² <<1 rapidity gap = log(1/x pom ) x pom <<1 target proton k: transverse momentum of the final-state gluon C. M., Nucl. Phys. B 705 (2005) 319 K. Golec-Biernat and C. M., Phys. Rev. D 71 (2005) 114005 1/k 0 : typical size at which the S-matrices are cut off observable strongly sensitive to unitarity effects measuring could select between saturation and Regge-based models 0k model dependent k²k² 1/k² model independent model independent k0k0 T qq and T qq (2)

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Diffractive jet production (2) k max /Q S = independent of Q², Q S 1.5 saturation predictions for HERA:

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RHIC phenomenology see Larry McLerran’s talk tomorrow quark-antiquark pair production see Hiro Fujii’s talk sunday recent review on particule production and saturation at RHIC: J. Jalilian-Marian and Y. Kovchegov, hep-ph/0505052

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Particule-production cross-sections are sensitive to the small-x regime of QCD they contain important complementary information w.r.t. DIS for T qq but also for T gg, T qqg, … on impact parameter/momentum transfer dependence Diffractive vector meson production at HERA: saturation models with ansatz for the impact parameter profile work quite well but that is not evidence for saturation need to start working with the momentum transfer Jet production in diffraction at HERA: great place to look for saturation effect can distinghuish between soft models and saturation Conclusions

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Universality of T qq : there are several parametrizations for T qq but could we describe everything that T qq should describe with only one? new global analysis Has RHIC really provided evidence for saturation? waiting for the LHC or listen to Larry McLerran tomorrow Outlook

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RHIC phenomenology see also Larry McLerran’s talk tomorrow see recent review: J. Jalilian-Marian and Y. Kovchegov, hep-ph/0505052

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R. Baier, A. Kovner and U. Wiedemann, Phys. Rev. D 68 (2003) 054009 D. Kharzeev, Y. Kovchegov and K. Tuchin, Phys. Rev. D 68 (2003) 094013 E. Iancu, K. Itakura and D. Triantafyllopoulos, Nucl. Phys. A 742 (2004) 182 J.P. Blaizot, F. Gélis and R. Venugopalan, Nucl. Phys. A 743 (2004) 13 J.Albacete, N. Armesto, A. Kovner, C. Salgado and U. Wiedemann, Phys. Rev. Lett 92 (2004) 082001 Nuclear modification factor in deuteron-gold collisions (1) with the parton-level cross-section predictions with a toy-model for T gg and with a numerical solution of the BK equation

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Nuclear modification factor in deuteron-gold collisions (2) first comparisons to the data: D. Kharzeev, Y. Kovchegov and K. Tuchin, Phys. Lett. B 599 (2004) 23 D. Kharzeev, E. Levin and M. Nardi, Nucl. Phys. A 747 (2005) 609 A. Dumitru, A. Hayashigaki and J. Jalilian-Marian, hep-ph/0506308 recent work: shows the importance of both x and DGLAP evolutions shows the importance of the quark component

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Azimutal correlations D. Kharzeev, E. Levin and L. McLerran, Nucl. Phys. A 748 (2005) 627 J. Jalilian-Marian and Y. Kovchegov, Phys. Rev. D 70 (2004) 114017 N. Nikolaev, W. Schäfer, B. Zakharov and V. Zoller, hep-ph/0504057 R. Baier, A. Kovner, M. Nardi and U. Wiedemann, hep-ph/0506126 but: correlators with product of up to four Wilson lines enter in the formulation of the cross-section preliminary data: predictions using kT-factorization assumption

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Other Observables Dilepton production electromagnetic probe very clear signal, no fragmentation function but need data Heavy quark production see Hiro Fujii’s talk sunday N. Armesto and M. Braun, Eur. Phys. J C22 (2001) 351 B. Kopeliovich and A. Tarasov, Nucl. Phys. A 710 (2002) 180 K. Tuchin, Phys. Lett. B 593 (2004) 66 N. Nikolaev and W. Schäfer, Phys. Rev. D 71 (2005) 014023 J.P. Blaizot, F. Gélis and R. Venugopalan, Nucl. Phys. A 743 (2004) 57 B. Kopeliovich, J. Raufeisen and A. Tarasov, Phys. Lett. B 503 (2001) 91 F. Gélis and J. Jalilian-Marian, Phys. Rev. D 66 (2002) 094014 M. Betemps, M. Gay Ducati, M. Machado and J. Raufeisen, Phys. Rev. D 67 (2003) 114008 R. Baier, A. Mueller and D. Schiff, Nucl. Phys. A 741 (2004) 358

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

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