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Quarkonia: theoretical overview

III Convegno Nazionale sulla Fisica di ALICE Frascati, 12-14 Novembre 2007. Quarkonia: theoretical overview. Marzia Nardi INFN Torino. CGC effects on J/ y production in nuclear collisions. p(d)-A : D. Kharzeev, K. Tuchin, hep-ph/0510358 (published)

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Quarkonia: theoretical overview

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  1. III Convegno Nazionale sulla Fisica di ALICE Frascati, 12-14 Novembre 2007 Quarkonia: theoretical overview Marzia Nardi INFN Torino

  2. CGC effects on J/y production in nuclear collisions p(d)-A : D. Kharzeev, K. Tuchin, hep-ph/0510358 (published) A-A : D. Kharzeev, E. Levin, M.N., K. Tuchin (in preparation)

  3. Hadron scattering at high energy From HERA: At high energies hadrons appear dense. A new phenomenon is expected : parton saturation Marzia Nardi

  4. Saturation scale in nuclei • [D.Kharzeev, E.Levin, M.Nardi] • Consider a nucleus or hadron interacting with an external probe, exchanging Q • Transverse area of a parton ~ 1/Q2 • Cross section parton-probe : s ~ as/Q2 • If many partons interact : S~Npartons • In a nucleus : NA=NpartonA [Nparton = xG(x,Q2)] • The parton density saturates when S~pRA2 • Saturation scale : Qs2 ~ as(Qs2)NA/pRA2 ~A1/3 • At saturation NA is proportional to 1/as • Qs2 is proportional to the (transverse) density of participating nucleons nA=NA/pRA2; larger for heavy nuclei. • NA~ Qs2 /as(Qs2) Marzia Nardi

  5. Color Glass Condensate Classical effective theory : high density limit of QCD • color : partons are colored • glass : they evolve slowly compared to their natural time-scale • condensate : their density is proportional to the inverse of the coupling constant, typical of a Bose condensate. Marzia Nardi

  6. Hadron production from the CGC Hadron multiplicities can be described in a parton saturation model, based on theColorGlass Condensatetheory. In particular : • Au-Au and d-Au collisions at RHIC, √sNN=20÷200 GeV • Pb-Pb and p-Pb collisions at LHC, √sNN= 5500 GeV • total multiplicity • centrality dependence • rapidity dependence Marzia Nardi

  7. J/y production The production mechanism of J/y in nuclear collisions at RHIC energies is different from that in pp collisions, because of gluon saturation in the nucleus. In p-A: • at forward y more suppression • at backward y weak enhancement Marzia Nardi

  8. mc > LQCD perturbative QCD, but non-perturbative effects are not negligible In A-A collisions: J/y suppression is a signature of QGP formation it is important to understand the production mechanism. At RHIC : experimental data on hadron multiplicity can be explained by CGC, parton (gluon) saturation in the nuclear wave function. Qs2(x2) >> LQCD. For heavy quarks : • Qs < m : Q production is incoherent, pQCD • Qs > m : Q production is coherent, the projectile interacts with the whole nucleus. Marzia Nardi

  9. Time scales in p-A collisions • tp = c-cbar production time • in the pair rest frame tp0 = 1/2mc . • in the nucleus rest frame (g=Eg/2mc) : tp =Eg/(2mc)2 Eg = x1 Ep s=(x1pp+x2pt)2=2x1x2EpM=2x2EgM s=(2mc)2 tp =1/(2x2M) x2=mce-y/sqrt(s) at RHIC : x2=6.5x10-3 e-y tp =15 ey fm Marzia Nardi

  10. tint = interaction time = RA/c at high energies tp > tint or lc=tp c > RA tp =15 ey fm : at forward y tp is very large • the projectile interacts with the whole nucleus • eikonal approximation for the calculation of scattering amplitude Marzia Nardi

  11. tf = J/y formation time • in the pair rest frame tf0= 2/(my’-my) • in the nucleus rest frame (g=Eg/My) : tf = 2Eg/(my’-my) My • tf0=0.45 fm  tfRHIC=41 ey fm Marzia Nardi

  12. At y>1, at RHIC : tf > tp > tint J/y is formed outside the nucleus, no nuclear effects ! Marzia Nardi

  13. At -1<y<0 the production time at RHIC becomes smaller than he nuclear size : the c-cbar pair is produced in the interaction with a few nucleons: enhancement of J/y production. Correction for nuclear absorption. A-A : as6A2/3 p-A : as5A1/3 For large A, diagram (a) dominates Marzia Nardi

  14. At y<-2 the coherence is lost. The production of J/y in p-A is similar to the one in pp collisions J/y can be formed inside the nucleus. c-cbar and J/y interact with nuclear matter. Marzia Nardi

  15. J/y production cross-section Marzia Nardi

  16. Probability of gluon radiation by a valence q: with • J/y wave function (NR approximation) Marzia Nardi

  17. The saturation properties are contained in the amplitude with Marzia Nardi

  18. Total cross-section where z=mr . • If My>Qs : and • If My<Qs : and Marzia Nardi

  19. Results for d-Au Marzia Nardi

  20. Marzia Nardi

  21. Marzia Nardi

  22. Results for Au-Au (RHIC) Marzia Nardi

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