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

2. 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

3. Introduction

4. 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

5. 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)

6. High-energy QCD (the Regge limit)

7. 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

8. 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

9. 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

10. 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

11. HERA phenomenology for particule production  * -proton collisions

12. 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

13. 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

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. 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)

17. 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)

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

19. 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

20. 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

21. 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

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

23. 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

24. 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

25. 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

26. 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