1. Comprehensive Analysis of In-Medium Quarkonia at SPS, RHIC + LHC Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, TX USA With: X. Zhao, A. Emerick Quark Matter 2012 Conference Washington (DC), 12.-18.08.12

2. 1.) Introduction: A “Calibrated” QCD Force  Vacuum charm- + bottomonium spectroscopy well described Non-perturbative force (E B Coul (J/  ) ~ 0.05 GeV vs. 0.6 GeV expt.) Persists in medium to at least ~2T c Potential approach in medium? [Kaczmarek et al ‘03] V [½ GeV] r [½ fm]

3. Lippmann-Schwinger equation In-Medium Q-Q T-Matrix: - 2.) Thermodynamic T-Matrix for Quarkonia in QGP [Mannarelli,Cabrera,Riek+RR ‘05,‘06,‘10] potential V  strictly real imaginary parts: unitarization (cuts in in-med. QQ propagator G QQ ) - q gluo-dissosciation (coupled channel) [Bhanot+Peskin ‘85] Landau damping (HQ selfenergy)

4. 2.2 Brueckner Theory of Heavy Quarks in QGP 2-body potential QQ T-matrix Qq T-matrix Q → Q 0-modes Quark selfenergy QQ evolution (rate equation) Q spectra + v 2 (Langevin) spectral fcts./ eucl. correlat. quark-no. susceptibility lattice data exp. data Input Process Output Test - -

5. reaction rate equilibrium limit (  -width) 3.) Transport Approach to Quarkonium Evolution J/  D D - c - c [PBM et al ’01, Gorenstein et al ’02,Thews et al ’01, Grandchamp+RR ’01, Ko et al ’02, Cassing et al ’03, Zhuang et al ’05, …] J/  + g c + c + X ← → - Regeneration in QGP + HG: detailed balance:  mc*mc* BB Input from T-Matrix (weak/strong binding) Rate Equation:

6. 3.1 Inputs + Parameters Input - J/   c,  ’, bb + cc production cross sections [p-p] - “Cold Nuclear Matter” effects (shadowing, nucl. abs., Cronin) [p/d-A] - Medium evolution: thermal fireball [A-A, hydrodynamics] Parameters - strong coupling  s controls  diss - incomplete c-quark equilibration: N  eq (  ) ~ N  therm (  ) · [1-exp(-  /  c eq )] - q -

7. 3.2 Inclusive J/  at SPS + RHIC  s ~0.3, charm relax.  c eq = 6(3) fm/c for U(F) vs. ~5(10) from T-matrix different composition in two scenarios Strong Binding (U) Weak Binding (F) [Zhao+RR ‘10]

8. 3.2.2 J/  p T Spectra + Elliptic Flow at RHIC small v 2 limits regeneration, but does not exclude it [Zhao+RR ‘08 ] (U potential) shallow minimum at low p T high p T : formation time, b feeddown, Cronin

9. 3.3 J/  at LHC: Centrality regeneration increases, still net suppression uncertainty from “shadowing” good consistency of transport approaches [Zhao+RR ‘11 ] Mid-Rapidity Forward Rapidity

10. 3.3.2 J/  at LHC: p T -Spectra + v 2 maximum at low p T confirms expected regeneration level room for additional regeneration with harder p T spectra… b-feeddown prevalent at high p T

11. 3.4  (1S) and  (2S) at LHC sensitive to color-screening + early evolution times clear preference for strong binding (U potential)  (1S) →  (2S) → [Grandchamp et al ’06, Emerick et al ‘11] Weak Binding Strong Binding

12. 4.) Conclusions Thermodynamic T-matrix approach → quarkonium spectral fcts. + HQ transport in QGP, benchmarks: lattice QCD, vacuum spectroscopy, pQCD Kinetic rate equation with in-medium quarkonia → dissociation + formation in QGP / hadronization inputs: HQ cross-secs., cold-nuclear-matter effects,… “Weak-binding” scenario disfavored - inconsistent with: HF transport,  (1S) suppression, … Manifestations of J/  regeneration - R AA SPS (T i ~220) ~ R AA RHIC (T i ~350) < R AA LHC (T i ~550) ~ 0.5 - low-p T enhancement of R AA LHC, finite v 2

13. 3.3.3 J/  at LHC III: High-p t – ATLAS+CMS underestimate for peripheral (expected from RHIC) (spherical fireball reduces surface effects …) [Zhao+RR ‘11 ]

14. 3.3.4 Time Evolution of J/  at LHC finite “cooking-time” window, determined by inelastic width [Zhao+RR ‘11 ] Strong Binding (U) Weak Binding (F)

15. 3.4  at RHIC and LHC sensitive to color-screening + early evolution times RHIC → LHC → [Grandchamp et al ’06, Emerick et al ‘11] Weak Binding Strong Binding

16. U-potential, selfconsist. c-quark width Spectral Functions - J/  melting at ~1.5T c -  c melting at ~T c -  c ~ 100MeV Correlator Ratios - rough agreement with lQCD within uncertainties 3.2 Charmonia in QGP: T-Matrix Approach [Mocsy+ Petreczky ’05+’08, Wong ’06, Cabrera+RR ’06, Beraudo et al ’06, Satz et al ’08, Lee et al ’09, Riek+RR ’10, …] [Aarts et al ‘07]

17. selfcons. c-quark width Spectral Functions - J/  melting at ~1.1T c -  c melting at ≤ T c -  c ~ 50MeV Correlator Ratios - slightly worse agreement with lQCD 3.2.2 T-matrix Approach with F-Potential [Riek+RR ’10] [Aarts et al ‘07]

18. 3.3 Charm-Quark Susceptibility in QGP sensitive to in-medium charm-quark mass finite-width effects can compensate in-medium mass increase [Riek+RR ‘10] 2 → →  → 0 m « T

19. 4.2.5.2 Thermalization Rate from T-Matrix thermalization 4 (2) times faster using U (F) as potential than pert. QCD momentum dependence essential (nonpert. effect ≠ K-factor!) [Riek+RR ‘10]  c [1/fm]

20. 4.5 Summary of Charm Diffusion in Matter Shallow minimun around T c ?! Quark-Hadron Continuity?! 20% reduction by non-perturbative HQ-gluon scattering Hadronic Matter vs. QGP vs. Lattice QCD (quenched) [He et al ’11, Riek+RR ’10, Ding et al ‘11, Gavai et al ‘11] AdS/CFT

21. dashed lines: gluo-dissociation solid lines: quasifree dissociation similar to full NLO calculation 3.1.3 Momentum Dependence of Inelastic Width _ [Zhao+RR ‘07] [Park et al ‘07]

22. 4.3 J/  at Forward Rapidity at RHIC [Zhao+ RR ‘10]