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Particule production and saturation

Particule production and saturation. Cyrille Marquet SPhT, Saclay. ISMD 2005, Kromeriz, Czech Republic. Contents. Introduction Bjorken limit and Regge limit of perturbative QCD

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Particule production and saturation

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

  2. Contents • IntroductionBjorken limit and Regge limit of perturbative QCD • High-energy QCD (the Regge limit) and saturationscattering matrix for high-energy partonsqq dipoles, gg dipoles, multipoles, … observables at small-x • HERA Phenomenologyforward jetsvector mesons, DVCSdiffractive jets • Conclusion and outlook

  3. Introduction

  4. Transverse view of the proton in DIS The Bjorken limit of pQCD Consider a collision of hadronic particules with a center-of-mass energy Wand a hard scale Q>>QCD The Bjorken limit: Q²  , W²   with Q²/W² fixed ( xBj in DIS) Operator product expansion At leading twist: collinear factorizationgluon distributionDGLAP evolution Higher twists suppressed by powers of Q² Scattering amplitudes decrease with increasing Q²

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

  6. High-energy QCD(the Regge limit)

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

  8. Dipoles and multipoles Instead of directly the Wilson lines, colorless combinations arise as the degrees of freedom: Tqq(x, x’,Y): the scattering amplitude of a qq dipole off the target: Tqq(x, x’; y, y’,Y): the scattering amplitude of two qq dipoles: Tgg(x, x’,Y): the scattering amplitude of a gg dipole: and more generally any multipole (2) We have denoted

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

  10. How does one compute Tqq, Tgg, Tqqg …? With • Y[A], and therefore Tqq, Tgg, Tqqg … 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 Observables at small-x More generally, any cross-section is a function of Tqq, Tgg, Tqqg … The more exclusive the final state is, the more complicated the corresponding multipoles are The same dipole amplitudes enter in the formulation of inclusive, diffractive, exclusive cross-sections 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

  11. HERA phenomenologyfor particule production * -proton collisions

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

  13. 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 need a parametrization for or Diffractive vector-meson production S. Munier, A. Stasto and A. Mueller, Nucl. Phys. B 603 (2001) 427 t = -q²

  14. 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)

  15. 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

  16. 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 Deeply Virtual Compton Scattering L. Favart and M. Machado, Eur. Phys. J C29 (2003) 365 Eur. Phys. J C34 (2004) 429 • they compute • they assume  Y = log(1/x) Bartels Golec-biernat Kowalski model

  17. model dependent rapidity gap  = log(1/xpom)xpom<<1 1/k0: 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 1/k² k² target proton k0 0 k model independent model independent Diffractive jet production (1) C. M., Nucl. Phys. B 705 (2005) 319 K. Golec-Biernat and C. M., Phys. Rev. D 71 (2005) 114005 Diffractive photon dissociation is the dominant contribution to the diffractive cross-section diff at large MX 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  = Q²/MX² <<1 (2)  Tqq and Tqq k: transverse momentum of the final-state gluon

  18. saturation predictions for HERA: Diffractive jet production (2) kmax/QS = independent of Q², QS  1.5

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

  20. Conclusions • Particule-production cross-sections are sensitive to the small-x regime of QCD they contain important complementary information w.r.t. DIS for Tqq but also for Tgg, Tqqg, … 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

  21. Outlook • Universality of Tqq:there are several parametrizations for Tqqbut could we describe everything that Tqq should describe with only one? new global analysis • Has RHIC really provided evidence for saturation? waiting for the LHCor listen to Larry McLerran tomorrow

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

  23. Nuclear modification factor in deuteron-gold collisions (1) 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 with the parton-level cross-section predictions with a toy-model for Tgg and with a numerical solution of the BK equation

  24. recent work: A. Dumitru, A. Hayashigaki and J. Jalilian-Marian, hep-ph/0506308 shows the importance of both x and DGLAP evolutions shows the importance of the quark component 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

  25. preliminary data: but: correlators with product of up to four Wilson lines enter in the formulation of the cross-section 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 Azimutal correlations D. Kharzeev, E. Levin and L. McLerran, Nucl. Phys. A 748 (2005) 627 predictions using kT-factorization assumption

  26. Other Observables • Dilepton productionelectromagnetic probe  very clear signal, no fragmentation functionbut need data • Heavy quark productionsee Hiro Fujii’s talk sunday 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 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

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