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V. Greco, LNS-INFN

Heavy Flavour at RHIC: Theoretical Perspective. V. Greco, LNS-INFN. Heavy Quarks and Jet Quenching Padova, 29 September 2005. Link to lQCD Relation to jet-quenching Prediction RHIC – LHC. gluon radiation (pQCD) collisional scattering (pQCD) resonant states (lQCD).

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V. Greco, LNS-INFN

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  1. Heavy Flavour at RHIC: Theoretical Perspective V. Greco, LNS-INFN Heavy Quarks and Jet Quenching Padova, 29 September 2005

  2. Link to lQCD • Relation to jet-quenching • Prediction RHIC – LHC • gluon radiation (pQCD) • collisional scattering (pQCD) • resonant states (lQCD) • Quarkonium as signature of a QGP phase: - J/Y, Y yields - Overview involved physics • Heavy-Quark jet-quenching : -different mechanism - RAA, v2 at RHIC (thermalization and quenching) - some prediction for LHC

  3. Specific of Heavy Quarks • use of pQCD for the initial production and quenching • lQCD calculation more reliable (quark loop damped) • Non-Relativistic EFT successful (see QG) • Use of the concept of potential -> bound states, resonances <-> lQCD -> fields effect in transport theory (plasma physics) • total # is frozen -> dN/dpt • we can have a plasma with rare and abundant ->dissolution & regeneration • Use Fokker-Planck to study collisional energy loss • Possibility to disentangle mass and charge effects in the gluon radiation (A. Dainese)

  4. Quarkoniumsuppression 4Tc Tc Coulomb -> Yukawa • In a QGP enviroment:(Matsui-Satz ‘86) • Color charge is subject to screening of the medium • -> qq interaction is weakened (short range) • Linear string term vanish in the confined phase • s(T) -> 0 deconfinement (long range) s-> 0 doesn’t mean no bound !

  5. Quarkonia States above Tc A(w)=w2r (w) Asakawa J/Y J/y (p = 0) disappears between 1.62Tc and 1.70Tc Similar results from potential model (Wong, Digal, Mannarelli) Y bottomonium Tdiss ~ 3-4 Tc Wong, hep-ph/0408020 Petrov,hep-lat/0503002

  6. In-medium suppression-regeneration • Lattice QCD heavy quark [Karsch] - Mass of quarkonia constant • In medium effective masses for charm quark and open charm • Low-lying charmonia survive in the QGP Increase suppression -> “new” mechanism Decrease of m*c,b and eBind Decrease regeneration -> Ny equil. decrease

  7. “new” mechanism In medium scattering Dynamical dissociation (QQ) + g Q + Q + X • Quarkoniadissociated also below TDiss • Lifetime of the QGP is essential gluon-dissociation, inefficient for my≈ 2 mc* “quasifree” dissoc. [Grandchamp ’01]

  8. Kinetic Evolution in HI Collisions ~ Statistical model • Kinetic approach – Rate equations: • Include in-medium effects (e(T), m*, s*) • Off-equilibrium features in the evolution • Chemical off-equilibrium: c • Incomplete thermalization Dominance of regeneration!

  9. Transition “direct suppressed”  “statistical” Excitation Function LHC ~10-2 (Thews) SPS RHIC Thews Regeneration over Initial production !

  10. Bottomonium at RHIC Grandchamp-Rapp,hep-ph/0507314 Gluon dissociation Quasi-free scattering 40% suppression No suppression • A smaller mass of mb -> NY equil. smaller • Screening effects enhances dissociation • -> 40% suppression over initial production • Regeneration negligible Y is a rather sensitive measure of Debye screening

  11. Bottomonium at LHC Quasi-free scattering Gluon dissociation Suppression 20% • A smaller mass of mb -> NY equil. smaller • Screening effects enhances dissociation • -> factor 7 suppression over initial production • Regeneration substantial Y is really a sensitive measure of Debye Screening

  12. Uncertainties: • - LHC dNch /dy ~ 3200 -1600 -> factor 7 -> 4 suppression • Bottom hadron spectrum: RHIC 15% – LHC (more) • Thermalization: RHIC (20%) – LHC (factor 2) • (regeneration component) The QGP of the lQCD lQCD potential model Microscopic Transport: Vqq+ scattering + gluon radiation + coalescence + fragmentation

  13. Regeneration is revealed in : • - pt-spectra • elliptic flow • charm at RHIC show sizable • collective properties. Quarkonium<->Heavy-quark In-medium energy loss studied by Open-Flavor Wang,PLB’02 • Excitation function of J/Y & Y (SPS-RHIC-LHC) is crucial to : • see suppression and regeneration -> QGP • see in medium effects -> lQCD but apart from uncertanties : • often there are alternative models : “RHIC data could be explained by the suppression of the c and Y’ components without recombination !!!” (M. Nardi - QM05) VG et al., PLB(2004)

  14. In Sky , in Earth and every place … Coalescence Well, except in the vacuum …

  15. Fragmentation: Parton spectrum • Leading parton pT ph= z pT according toa probability Dh(z) • z < 1, energy needed to create quarks • from vacuum ET ~ 730 GeV b(r)~ 0.5 r/R T ~ 170 MeV Coalescence: B M • partons are already there • ph= n pT ,, n = 2,3 • to be close in phase space $ V ~ 900 fm-3 e ~ 0.8 GeVfm-3 dS/dy ~ 4800 Coalescence vs. Fragmentation H Partonic Hydro behavior shifted at higher pT Even if eventually Fragmentationtakes over …

  16. Meson & Baryon Spectra Au+Au @200AGeV (central) sh V. Greco et al., PRL90 (03)202302 PRC68(03) 034904 R. Fries et al., PRL90(03)202303 PRC68(03)44902 R. C. Hwa et al., PRC66(02)025205 • Proton suppression hidden by coalescence! ReCo dominates up to 4-6 GeV/c; fragmentation and energy loss takes over above.

  17. Coalescence scaling Enhancement of partonic v2 Duke Elliptic Flow v2,q from a fit to p data -> v2 p, K, L ... prediction D. Molnar and S.A. Voloshin, PRL91 (03) w.f. effect 5% B/M breaking (Dp~0.25 GeV) Large breaking if Dp >> (OSU, PRC68) Shape consistent with cascade (AMPT, MPC) To be seen, breaking of the scaling !

  18. Quenching of heavy quarks • Collisional energy loss - neglected in the light quark sector • Induced gluon emission - mass effect (“dead cone”) - Ter-Mekayelian effect (in-mediumgluon dispersion relation) - transition radiation • Scattering on resonant states - suggestion from lQCD (spectral function & potential model) Mustafa, PRC72

  19. Gluon Radiation If significant suppression b+ce- b 0 g Mass effect -> reduction of quenching • Dead-cone effect (also in vacuum) • -Hind gluon emission atQ0< M/E • No gluon contribution to quenching • -Heavy flavor allow to disentangle • Color charge effect and mass effect • (A. Dainese) Interesting to see in the jet reconstruction (LHC) What will come out … Heavy -> smaller effects of cut-off in the soft gluon emission

  20. GLV Quenching Heavy Quarks-I Related to the heavy quark E-loss work: - mass effect (“dead cone”) - Ter-Mekayelian effect (in-medium gluon dispersion relation) - transition radiation ~ 30% -> 15 % (L~ 5 fm) TR TM Djordjevic’03-05

  21. GLV Quenching Heavy Quarks-II Parton Level RAA(pT) B B Parton Level RAA(pT) u,d u,d D D 0 g g pT [GeV] pT [GeV] RAA(e-) / RAA(0)> 3 RAA(e-) / RAA(0)> 2 According to our results, charm quark suppression should be small ~ 0.6-0.8. Therefore, this suppression should be definitely much smaller than the already observed pion suppression (0.2). (M.D. QM04) Moderate D mesonsuppression ~ 0.3-0.5at RHIC. We obtained that at pT~5GeV, RAA(e-)> 0.5±0.1at RHIC (M.D. QM05)

  22. RAA pT [GeV/c] Comparison with results by Armesto et al. Single electrons from Charm only reproduce Armesto et al. plots M. Djordjevic et al., hep-ph/0410372 N. Armesto et al. hep-ph/0501225

  23. Calculation of Collisional energy loss w(p,k) directed linked to the cross section g c q c [Svetitsky ’88, Braaten ’91, Mustafa etal ’98, Molnar etal ’04 Zhang etal. ’04, Teaney+Moore‘04] • dominated by t-channel gluon-ex in gc→gc: Drag & Diffusion p-indipendent scatt. rate diff. const. Transport Equation in quasi-particle approx. Expanding w(p,k) around p~k : dominated by soft scattering: (resonable for heavy quarks) Fokker-Plank equation Background not affected by heavy quarks

  24. pQCD scattering energy loss Infrared cut-off For heavy quarks: problem is better solved E<<M2/T (10 GeV) - only heavy Djordjevic (HTL- thermal mass) Mustafa,PRC72 Mustafa,PRC98 Bjorken ‘82 E>>M2/T Infrared ambiguity, solved by Braaten-Thoma’91 (soft scale with a dressed gluon, work for M>>T) Collisional energy loss is not negligible (Mustafa) The net effect depends also on fluctuation

  25. Fokker-Plank for charm interaction in a hydro bulk G.D. Moore and D. Teaney, nucl-th/0412346 Charm-pQCD (as, mD=1.5T) Too low RAA or too low v2 • hydro withTc=165, t ≈ 9-15fm/c • asand Debye mass independent Coalescence modify v2D- RAA correlation

  26. _ _ “D” q q c c “Light”-Quark Resonances 1.4Tc [Asakawa+ Hatsuda ’03] Open-Charm Resonances in QGP [van Hees+ Rapp ’04] J/Y • effective model with pseudo/scalar • + axial/vector “D-mesons” • number of D-states: 4 u and d, 2 s • cross section isotropic • more microscopic • from lQCD potential→[M.Mannarelli‘04]

  27. Thermalization w “D”-Mesons • Heavy-Quark Effective Field Theory (HQEFT): • Chiral (u,d) and Heavy quark symmetry (c) • assuming D meson chiral restored bound states [van Hees+RR ’04] pQCD “D” Few hadron resonances above Tc -> generalization of coalescence Isotropic angular distribution sres essential for thermalization

  28. Heavy-Flavor Baseline Spectra at RHIC D-Mesons Single-Electron Decays • bottom crossing at 5GeV !? (pQCD: ~4GeV[Cacciari etal ’05]) • strategy: fix charm with D-mesons, • adjust bottom in e±-spectra

  29. Heavy-Quark and Electron Spectra at RHIC → stochastic implementation of heavy quarks in expanding fireball with realistic time evolution of bulk v0 , v2 Nuclear Suppression Factor Elliptic Flow • characteristic “leveling-off” • factor ~4 from resonances • pQCD elastic scatt. moderate • resonance effects substantial

  30. Single-Electronv2andRAAat RHIC coalescence + fragment. fq from p, K Nuclear Suppression Factor Elliptic Flow Minimun-Bias Au-Au 200GeV Minimun-Bias Au-Au 200GeV • coalescence increases both RAA and v2,resonances essential • bottom contribution reduces effects • induced gluon radiation should be included (additive ?)

  31. Fragmentation only • Uncertainties: • Charm quark mass • coalescence/fragmentation ratio • fragmentation of charm quarks • Improvements: • include gluon radiation • better estimate of B/C cross sections • no-sudden coalescence • Lower (better) RAA but also lower v2

  32. Therm +flow pQCD statistical Baryon/meson from coalescence Quarkonia v2 from regeneration • Contamination in single e : v2Lc > v2D • BR to single electrons 4.5% • -> contamination negligible • cut if one can verify those prediction …

  33. Tracing the Waker ? f Near-side Away-side Problem how to go from gluon wave to hadron? • Excitations of 1) colorless (hydrodynamical) modes => Mach cones J. Casalderray, E. Shuryak, D. Teaney, hep-ph/0411315 • 2) colorful modes: 2.1) longitudinal modes => Mach conesH. Stöcker, NPA750(2005), J. Ruppert, B. Müller, PLB618 (2005) • 2.2) transverse modes =>Cherenkov (like) radiation I. Dremin, hep-ph/0507167, A. Majumder, nucl-th/0507062 • Medium evolution of radiated gluonsS. Pal and S. Pratt, PLB574 (2003) • Unique to heavy quark : • Tag the jet distinguishable from the gluon wave • ->jet cannot be reabsorbed • Angular correlation of jets sensitive to quenching mechanism • ->radiative vs resonant (calculation needed) • 3 particle correlations with 2 particle in the away-side: • ->for heavy-quarks in the away side one can look at jet itself pTtrig=4-6 GeV/c pTassoc=0.15-4 GeV/c

  34. Prediction from energy loss (single scattering) for LHC

  35. Prediction for LHC from Jet-Quenching L=6 fm RHIC LHC (PHOBOS) LHC (CGC) M. Djordjevic et al., PRL94 (2005) • Increases Eloss compensated by decreased slope of quark distributions • -> RAA not very sensitive to dN/dy in a gluon radiation scenario ? What happens with D-like (T< 2 Tc) and B-like (T<4 Tc) resonant states

  36. Summary No suppression Factor 4-7 • Quarkonia yield tightly linked to lQCD : • Y yield very sensitive to QGP-QCD • Quarkonia by coalescence <-> b,c jet quenching : • more than pQCD elastic scattering – charm close to thermalization • Coalescence relevant for RAA- v2 open charm • - disentangle gluon radiation & resonant scattering • - Di-jet correlation with heavy quarks • possibility to infer QGP structure in the heavy-light sector • - Effect of appearance disappearance of resonant states at LHC? • mass effect LHC <-> weak evolution (according to GLV) • Dileptons should be even more sensitive ( new calculation afterRHIC data on open charm)

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