Quarkonium Correlators in Medium

1. 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), 19.10.07

2. _ Q-Q Potential Scattering Rates Q Selfenergy 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) • pT-spectra, v2(pT) Theory:- in-medium -spectral functions - Euclidean correlators: lattice QCD ↔ effective models

3. Outline 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 3.2In-Medium HQ Masses 3.3Width Effects 4.) Charmonia at RHIC 5.)Summary + Outlook

4. 2.1 Euclidean Correlator + Timelike Spectral Function Early Example: Dileptons (r, w) integrate [Wetzorke et al ‘01] [RR ‘01] • schematic at the time

5. 2.1.2 Lattice QCD Computations: G / Grecon+ SFs • accurate “data” from lattice QCD hc cc [Datta et al ‘04] • S-wave charmonia little changed to ~2Tc, P-wave signal enhanced(!) • similar in other lQCD studies [Iida et al ’06, Jakovac et al ’07, Aarts et al ’07]

6. - Q-QT-Matrix: 2.2 Potential-Model Approaches for Spectral Fcts. s/w2 • Schrödinger Eq. for bound • state + free continuum • sy(w) = Fy2d(w - my )+w2Q(w-Ethr) fythr • - improved for rescattering J/y [Shuryak et al ’04, Wong ’05, Alberico et al ’05, Mocsy+Petreczky ’05] Y’ cont. w [Mocsy et al ’06, Laine ’07, Wong et al ’07, Alberico et al ‘07] Ethr • Lippmann-Schwinger-Eq. • for [Mannarelli+RR ’05,Cabrera+RR ‘06] - 2-quasi-particle propagator: - bound+scatt. states, nonperturbative threshold effects (large!) • Correlator: L=S,P

7. 2.3.1 Uncertainties I: “Lattice QCD-based” Potentials • free vs. internal energy: F1 (r;T) = U1(r;T) – T S(r;T) • (much) smaller binding for • V1=F1, V1 = (1-a) U1 + a F1 [Cabrera+RR ’06; Petreczky+Petrov’04] [Wong ’05; Kaczmarek et al ‘03]

8. 2.3.2 Uncertainties II: Heavy-Quark Masses in the QGP • quarkonium mass:my= 2mc* - eB • asymptotic energiesF∞ = U∞ - TS∞ U∞ [Kaczmarek +Zantow ‘05] F∞ • close toTc: - increasing heavy-quark mass?! • - entropy contribution?

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

10. 3.1 Baseline Results:V1=U1, mc=1.7GeV fix, Gy small, Grec= Gvac - Q-QT-Matrix • ~40% variation in S-wave (1.1Tc overbound), P-wave: zero modes needed hc cc • slightly overbound at 1.1Tc • (or mc too small) • dissolves at >2.5Tc • quickly dissolves above Tc

11. 3.2 T-Matrix with in-medium mc* - I • lattice U1-potential, mc* from U1subtraction hc • upward shift due to large mc* at 1.1Tc • ~stable my=2mc*-eBabove → correlator within ~20%

12. 3.2.2 T-Matrix with in-medium mc* - II • lattice U1-potential, adjust mc* close to Tc + zero modes;S-Waves: [Cabrera+RR in prep] T-Matrix Approach [Aarts et al. ‘07] Lattice QCD J/y hc • fair agreement!

13. 3.2.3 T-Matrix with in-medium mc* - II • lattice U1-potential, adjust mc* close to Tc + zero modes; P-Waves: [Cabrera +RR in prep] T-Matrix Approach [Aarts et al. ‘07] Lattice QCD cc0 cc1 • fair agreement!

14. 3.2.4 Temperature Dependence of Charm-Quark Mass • significant deviation only close to Tc

15. _ • effect on correlator • moderate width • → small enhancement hc [Cabrera+RR ‘06] 3.3 Finite-Width Effects • c-quark width in propagator • dominant process depends on eB J/y Lifetime [Grandchamp+RR ‘01]

16. 4.) Observables at RHIC: Centrality + pT Spectra • updated predictions including 3-momentum dependencies [X.Zhao+ RR in prep] • balance direct - regenerated • sensitive to: mc* , Ncc

17. 5.) Summary • potential models useful tool to interpret finite-T lQCD • importance of nonperturbative threshold effects • consistency of bound+scatt. states + mc* mandatory (T-matrix) • significant uncertainties (U1 vs. F1 , mc*) • S-wave charmonia survival to2-3Tcin line with lQCD correlators • no conclusive interpretation yet: • threshold reduction compensates decreasing binding • quarkonium lifetimes of tY ≤ 1fm/c possibly relevant

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

19. 3.3.2 Observables II: Excitation Function + Rapidity J/ySuppression vs. Regeneration SequentialY’+cc Suppression [Grandchamp +RR ’01] [Karsch,Kharzeev+Satz ‘06] • direct J/yessentially survive • (even at RHIC) • nontrivial “flat” dependence • similar interplay in rapidity!? • (need accurate dNc/dy)