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Heavy-Flavor Probes of Quark-Gluon Plasma and RHIC

This presentation discusses the use of heavy quarks (c and b) as probes of the Quark-Gluon Plasma (QGP) in heavy-ion collisions. It covers topics such as heavy quarkonia, heavy-quark diffusion, and quarkonium production in ultra-relativistic heavy-ion collisions. Theoretical and phenomenological constraints are discussed, along with the effects of the thermal medium on heavy quarks.

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Heavy-Flavor Probes of Quark-Gluon Plasma and RHIC

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  1. Heavy-Flavor Probes of Quark-Gluon Plasma and RHIC Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA CATHIE/TECHQM Workshop BNL (Upton, NY), 16.12.09

  2. 1.) Introduction: Virtues of Heavy Quarks(c,b) • “Large” scale mQ >> LQCD , T • - factorization in production; thermal medium: pth2 ~ 2mQ T >> T2 • Interactions spacelike (“low” pt): • - quarkonia ↔ potential QCD • - heavy-quark diffusion ↔ elastic scattering, Fokker-Planck • → unified framework • Beyond perturbation theory (as expansion) • → resummations, bound + scattering states • Theoretical / phenomenological constraints essential • Heavy-ion collisions: • - initial-state effects (shadowing, absorption, formation time, …) • - medium effects: equilibrium properties, expansion collectivity

  3. Outline 1.) Introduction 2.) Heavy Quarkonia in QGP  Thermal Lattice QCD  Potential Models  “Corrections” 3.) Quarkonia in Heavy-Ion Collisions  Thermal Rate Equation  Suppression, Regeneration + “Tdiss” 4.) Heavy-Quark Diffusion in QGP  Fokker-Planck + T-Matrix  Heavy-Quark Observables at RHIC 5.) Conclusions

  4. 2.1 Quarkonium Correlators in Lattice QCD • direct computation of • Euclidean Correlation Fct. • accurate lattice “data” spectral function [Datta et al ‘04] hc J/y [Aarts et al ’07] • ~20% variation of S-wave charmonia ~ 0.9-3 Tc • Bound states survive? Spectral functions?! [Asakawa et al ’03, Iida et al ’06, Jakovac et al ‘07]

  5. 2.1.2 Heavy-Quark Free Energy in Lattice QCD • F1(r,T) = U1(r,T) – T S1(r,T) • V(r,T) ≡ X1(r,T) - X1(r=∞,T) • X1∞/2 ~ DmQ(T) (?) • examples: • (a) X1= F1 • => weak potential, eB(1.1Tc) ~ 50 MeV • DmQ(T)small • (b) X1=U1( U = ‹Hint› ) • => strong potential,eB(1.1Tc) ~ 500 MeV • DmQ(T)large • approximate compensation in • bound-state mass: Ey = 2mc0 + X1∞-eB [Kaczmarek+Zantow ’05]

  6. 2.1.3 In-Medium Charm-Quark Mass in LQCD [Kaczmarek +Zantow ’05] [Velytsky et al ’09] F • U: large variation close toTc • – mass interpretation?! • fit quark-number fluctuations with • zero-width quasiparticle model • c(T) ~ ∂2P / ∂2mc

  7. 2.2 Potential Models for Spectral Functions • well established in vacuum (EFT, lattice) • Schrödinger equation in medium • correlators: quark rescattering in continuum [Shuryak+Zahed ’04, Mocsy+Petreczky ‘06, Alberico et al ‘06, Wong ’07, Laine ’07, Ghiglieri et al ‘08…] • Lippmann-Schwinger equation [Mannarelli+RR ’05, Cabrera+RR ‘06] In-Medium Q-QT-Matrix: - - - Q-Q propagator: - bound + scattering states (threshold enhancements)

  8. mc=1.7GeV mc* 2.2.2 Potential Models in the QGP [Mocsy+ Petreczky ’05,‘08] [Cabrera +RR ‘06] ~F1potential U1potential hc mc=1.7GeV • F1 low threshold (2mc~ 2.7GeV), • ground state Tdiss ~ 1.2 Tc • U1 decreasing threshold and eB, • Tdiss ~2.5Tc •  both scenarios compatible with lat-QCD

  9. q q 2.3 Quarkonium Widths in QGP → sensitive to binding energy (i.e., color screening) J/y Dissociation Rates NLO anti-/quarks NLO gluons as~0.25 as~0.5 [Grandchamp+RR ’01] [ Park et al ’07] • inelastic J/y width ~ (50-500) MeV

  10. 2.4 Further “Corrections” to Spectral Functions • Relativistic effects • - kinematics • - magnetic interaction → “Breit” correction: • VQ1Q2(r) → VQ1Q2(r) ( 1 – v1 · v2 )(↔ Poincaré-invariance, pQCD) • Retardation effects • - 4-D → 3-D reduction of Bethe-Salpeter equation • - energy transfer fixed (usually q0=0), off-shell behavior ambiguous • Gauge dependence of color-singlet free energy • Field-theoretic ansatz: • [Megias et al ’07] • color-Coulomb: vector , string: • - fit color-average free energy to lQCD, extract Fa , Ua scalar •  implement into “extended T-Matrix approach” [Brown et al ‘05] [Philipsen ‘08] [Riek+RR in prep]

  11. 2.4.2 Example from “Extended T-Matrix Model” S-Wave Spectral Function Euclidean Correlator Ratio hc - • ccpropagator with Gc= 100 MeV: • S-wave “melting” Tdiss ≈ 1.5-2 Tc • correlator ratio temperature-stable

  12. Regeneration in QGP + HG: • - backward reaction (detailed balance!) if J/y survives → - ← J/y + g c + c + X [PBM et al ’01, Gorenstein et al ’02,Thews et al ’01, Grandchamp+RR ’01, Ko et al ’02, Cassing et al ’03, Zhu et al ’05, …] D - D J/y reaction rate equilibrium limit (y -width) - c c (links to spectral function) J/y 3.) Quarkonium Production in URHICs • 3-Stage Dissociation:nuclear (pre-eq) -QGP-HG • Stot = exp[-snucrL] exp[-GQGPtQGP ] exp[-GHGtHG ]

  13. 3.1.2 J/y Spectral Functions (schematic) Inelastic Width Spectral Function “Weak-Binding” Scenario “Strong-Binding” Scenario - • T>Tdiss : J/y → cc , • no formation • J/y mass =3.1GeV const • ↔ equilibrium limit

  14. 3.1.3 Equilibrium Limit (Statistical Model) - • fixed c-c number: • equilibrium • Y number: • (very) sensitive to • open-charm spectrum • thermal relaxation for • c-quark spectra: [Grandchamp et al ’03, Andronic et al ’07, …]

  15. 3.1.4 Initial Condiations + Medium Evolution - • J/y (cc, y’), c-c production cross sections [p-p data, pQCD, …] • Cold Nuclear Matter effects: • - shadowing • - nuclear absorption • - pt broadening [p-A data, CGC, …] • (Thermal) fireball evolution: • - thermalization time (↔ initialT0), Tc • - expansion rate, lifetime, freezeout, … [hadron data, • hydrodynamics, transport,…] [Kharzeev et al ‘07, Ferreiro et al ‘08]

  16. 3.2 Charmonium at RHIC: Centrality Dependence • solve rate equation with thermal fireball,T0 = 310-340 MeV(MB-central) Strong-Binding Scenario Weak-Binding Scenario • weak-binding requires faster c-quark relaxation (tceq=9vs. 3 fm/c) • strong-binding favored? [Zhao+RR ‘09]

  17. 3.2.2 Comparison of Thermal Rate-Eqs. at RHIC RAA Nucl. Abs. 4 mb|0 mb Medium Evo. fireb. | hydro Width NLO+ | LO + direct |1/Q(T-Td) 2.5Tc|1.9Tc <pt 2> [Zhao+RR ‘09] [Liu,Qu,Xu+ Zhuang ‘09] • good agreement but different in detail • see also [Gunji et al ’07, Young et al ’09,…]

  18. pQCD elastic scattering:g-1= ttherm ≥ 20 fm/cslow q,g c [Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore ’04, Peshier,Gossiaux+Aichelin ‘09] • In-medium heavy-light T-matrix: direct connection to quarkonia! [van Hees et al ’07, Riek et al in prep] 4.) Heavy-Quark Diffusiion in the QGP • Brownian • Motion: Fokker Planck Eq. [Svetitsky ’88,…] Q thermalization rate diffusion coefficient

  19. 4.2 Charm-Quark T-Matrix + Thermalization Thermal Q-qT-Matrix Thermalization Rate • meson/diquark resonances for T <1.4Tc • thermalization rate ~ const

  20. 4.3 Thermalization Rate and Diffusion Coefficient g [1/fm] T [GeV] T [GeV] • “different” approaches related, e.g. AdS/CFT ↔ Coulomb • large coupling in pQCD calls for resummation • NB: suppression (RAA) early - elliptic flow (v2) “late”

  21. 4.4 Comparison of c-Quark RAA + v2 [26] [28] [115] [arXiv:0903.1096 hep-ph]

  22. 4.5 e± Spectra at RHIC T-mat T-mat T-mat T-mat [van Hees et al ‘07] • hadronic resonances at~Tc↔ quark coalescence • connects 2 “pillars” of RHIC: strong coupl. + coalescence

  23. 5.) Conclusions • Theoretical relations heavy quarks - quarkonia • - potential approaches (+ corrections) • - constraints from lattice QCD • (not yet conclusive: U1 ↔ Tcy~2Tc vs. F1 ↔ Tcy~1.3Tc) • - full heavy-quark(onium) many-body problem to be worked out • Quarkonium phenomenology • - “strong” J/y binding favored? (pt-data …) • - bottomonium suppression? • Open heavy flavor • - resonances close to Tc ? (strong coupling + coalescence…) • - RHIC non-photonic e± Ds (2pT) ≈ 5 , v2-RAA correlation • - scrutinize medium evolution, Fokker-Planck, d-Au …

  24. 3.2.3 Rapidity Dependence at RHIC Thermal Rate-Eq Approach • regeneration yield sensitive to dNc/dy • regeneration yield alone problematic • with pt-dependence • additional shadowing at forward y [Kharzeev et al. ‘07, Ferreiro et al. ‘08] [Zhao+RR ‘09]

  25. 1.2 J/y Suppression in Heavy-Ion Collisions • Universal suppression pattern at SPS and RHIC • as function produced-particle number?

  26. _ 2.3.2 Momentum Dependence of Inelastic Width • dashed lines: gluo-dissociation • solid lines: quasifree dissociation • similar to full NLO calculation [Park et al ‘07] [Zhao+RR ‘07]

  27. 3.2.4 Momentum Spectra and Elliptic Flow • regeneration at low pt → small v2 • direct component at high pt → small v2 [Zhao+RR ’08, Zhuang et al ‘06]

  28. high pT: formation time ( ), • bottom feeddown, … [Karsch+Petronzio ’87, Blaizot+Ollitrault ‘87] 3.2.5 Momentum Spectra Au-Au 200AGeV • regeneration part → blast-wave at Tc • regeneration at low pT [Zhao+RR ’07, ‘08]

  29. Satz, Digal, Fortunato Rapp, Grandchamp, Brown Capella, Ferreiro • Percolation • Plasma • Comovers NA60 preliminary 3.5 Charmonium Observables at SPS Pb(158AGeV)-PbIn(158AGeV) –In • QGP-suppression prevalent • “jumps” / ”plateaus” in centrality? [Grandchamp etal ’03]

  30. 2.2 Color Magnetic Interaction and Constraints • Color-Magnetic “Breit” Interaction • VQ1Q2(r) → VQ1Q2(r) ( 1 – v1· v2 ) [G.E. Brown ’52, Brown et al ‘04] - Vacuum “Spectroscopy” Perturbative Q-q Scattering mc0 =1.4 GeV - [van Hees et al ‘09] [Riek et al ‘09] - • Born approx. TQq = VQq • recovers pQCD within ~20% • Q-Q and Q-q states ~ o.k. • spin-interactionsO(1/mQ)

  31. 3.3.4 Rapidity Dependence at RHIC Statistical Model Thermal Rate-Eq Approach • reproduced in statistical hadronization • model (GC ensemble) [Andronic et al. ’07] • more problematic in dynamic • approaches • additional shadowing at forward y? [Capella et al. ’07, Zhao+RR ‘08] [Kharzeev et al. ‘07, Ferreiro et al. ‘08]

  32. 3.4 Upsilon at RHIC No Color-Debye Screening With Color-Debye Screening [Grandchamp et al. ’05] • (1S,2S) suppression unambiguous QGP signature ?! • NB: 50% feed-down on(1S)

  33. 3.3 Heavy-Quark Spectra at RHIC • relativistic Langevin simulation in elliptic expanding fireball background Nuclear Modification Factor Elliptic Flow pT [GeV] pT [GeV] • T-matrix approach ≈ effective resonance model • similar to “coll. dissoc.” [Adil+Vitev ’07]; radiative E-loss? (2↔3), …

  34. 2.2.1 Color Screening + Quarkonium Binding in QGP e.g. screened Cornell pot.: Charmonium Bottomonium ~Tc ~Tc m~ gT [GeV] [Matsui+Satz ’86, Karsch,Mehr+Satz ’88, Wong ’04, …] m~ gT [GeV] • quarkonium binding substantially reduced aboveTc

  35. 2.3.2 Bottomonium Reaction Rates in QGP • color-screening accelerates dissociation • significance at RHIC: tY ≈ 50 →5 fm/c [Grandchamp et al. ’05]

  36. 3.3.3 Dissociation Temperature Suppression only (Hydro) Including Regeneration Tdiss= 2.0 Tc 1.2 Tc “threshold melting” “finite width” [Zhao+RR ‘08] • finite width and regeneration • wash out “step” structure [Gunji et al. ‘07]

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