Quarkonium Correlators in Medium Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA Quarkonium Working Group Workshop QWG ‘07 Deutsches Elektronen Synchrotron (Hamburg),

1.) Introduction: Quarkonia Probing the QGP immerse -pair into the QGP  Vacuum properties change: color screening (reduced binding) dissociation reactions (and reverse!) heavy-quark mass (→ mass, decay rates, threshold) Experiment: Heavy-Ion Collisions yields; no access to spectral shape (?) mass ↔ equilibrium number ~ exp(-M/T) p T -spectra, v 2 (p T ) Theory: - in-medium -spectral functions - Euclidean correlators: lattice QCD ↔ effective models Q-Q Potential Scattering Rates Q Selfenergy _

1.) Introduction 2.) Potential Models + Spectral Functions 2.1 SFs + Correlators, Lattice Results 2.2 Potential Models (Schrödinger/T-Matrix) 2.3 Uncertainties in Potential + HQ Mass 3.) T-Matrix Approach 3.1 Baseline Results 3.2 In-Medium HQ Masses 3.3 Width Effects 4.) Charmonia at RHIC 5.) Summary + Outlook Outline

2.1 Euclidean Correlator + Timelike Spectral Function Early Example: Dileptons ( ,  ) integrate schematic at the time [RR ‘01] [Wetzorke et al ‘01]

2.1.2 Lattice QCD Computations: G / G recon + SFs accurate “data” from lattice QCD S-wave charmonia little changed to ~2T c, P-wave signal enhanced(!) similar in other lQCD studies [Iida et al ’06, Jakovac et al ’07, Aarts et al ’07] cc cc [Datta et al ‘04]

Correlator: L=S,P Lippmann-Schwinger-Eq. for Q-Q T-Matrix: Potential-Model Approaches for Spectral Fcts. [Mannarelli+RR ’05,Cabrera+RR ‘06] - 2-quasi-particle propagator: - bound+scatt. states, nonperturbative threshold effects (large!) Schrödinger Eq. for bound state + free continuum   (  ) = F  2  (   m  ) +  2   -  thr  f  thr - improved for rescattering  2  J/  ’’ cont. [Shuryak et al ’04, Wong ’05, Alberico et al ’05, Mocsy+Petreczky ’05] [Mocsy et al ’06, Laine ’07, Wong et al ’07, Alberico et al ‘07] E thr

2.3.1 Uncertainties I: “Lattice QCD-based” Potentials (much) smaller binding for V 1 =F 1, V 1 = (1-  U 1 +  F 1 free vs. internal energy: F 1 (r;T) = U 1 (r;T) – T S(r;T) [Cabrera+RR ’06; Petreczky+Petrov’04] [Wong ’05; Kaczmarek et al ‘03]

2.3.2 Uncertainties II: Heavy-Quark Masses in the QGP [Kaczmarek +Zantow ‘05] close to T c : - increasing heavy-quark mass?! - entropy contribution? quarkonium mass: m  = 2m c * -  B asymptotic energies F ∞ = U ∞ - TS ∞ U∞U∞ F∞F∞

3.) T-Matrix Approach 3.1 Baseline Results 3.2 In-Medium HQ Masses 3.3 Width Effects [Cabrera+RR ‘06]

3.1 Baseline Results: V 1 =U 1, m c =1.7GeV fix,   small, G rec = G vac Q-Q T-Matrix - cc cc slightly overbound at 1.1T c (or m c too small) dissolves at >2.5T c quickly dissolves above T c ~40% variation in S-wave (1.1T c overbound), P-wave: zero modes needed

3.2 T-Matrix with in-medium m c * - I lattice U 1 -potential, m c * from U 1 subtraction cc upward shift due to large m c * at 1.1T c ~stable m  =2m c *-  B above → correlator within ~20%

lattice U 1 -potential, adjust m c * close to T c + zero modes; S-Waves: T-Matrix with in-medium m c * - II J  cc T-Matrix Approach Lattice QCD [Cabrera+RR in prep] [Aarts et al. ‘07] fair agreement!

lattice U 1 -potential, adjust m c * close to T c + zero modes; P-Waves: T-Matrix with in-medium m c * - II  c1  c0 T-Matrix Approach Lattice QCD [Aarts et al. ‘07] [Cabrera +RR in prep] fair agreement!

3.2.4 Temperature Dependence of Charm-Quark Mass significant deviation only close to T c

3.3 Finite-Width Effects c-quark width in propagator dominant process depends on  B J/  Lifetime _ [Grandchamp+RR ‘01] [Cabrera+RR ‘06] moderate width → small enhancement effect on correlator cc

balance direct - regenerated sensitive to: m c *, N cc 4.) Observables at RHIC: Centrality + p T Spectra [X.Zhao+ RR in prep] updated predictions including 3-momentum dependencies

5.) Summary potential models useful tool to interpret finite-T lQCD importance of nonperturbative threshold effects consistency of bound+scatt. states + m c * mandatory (T-matrix) significant uncertainties (U 1 vs. F 1, m c *) S-wave charmonia survival to 2-3T c in line with lQCD correlators no conclusive interpretation yet: threshold reduction compensates decreasing binding quarkonium lifetimes of   ≤ 1fm/c possibly relevant

3-Stage Dissociation: nuclear (pre-eq) -- QGP -- HG S tot = exp[-  nuc   L] exp[-  QGP  QGP ] exp[-  HG   HG ] Regeneration in QGP + HG: - microscopically: backward reaction (detailed balance!) key ingredients: reaction rate equilibrium limit (  -width) (links to lattice QCD) 4.) Suppression + Regeneration in Heavy-Ion Collisions [PBM etal ’01, Gorenstein etal ’02,Thews etal ’01, Grandchamp+RR ’01, Ko etal ’02, Cassing etal ‘03] J/  + g c + c + X ← → - - for thermal c-quarks and gluons:  -  nuc (SPS) ≈ 4.5mb - RHIC d-Au data →  nuc ≈ 0-3mb

nontrivial “flat” dependence similar interplay in rapidity!? (need accurate dN c /dy) Observables II: Excitation Function + Rapidity J/  Suppression vs. Regeneration [Grandchamp +RR ’01] direct J/  essentially survive (even at RHIC) Sequential  ’+  c Suppression [Karsch,Kharzeev+Satz ‘06]