Comprehensive Analysis of In-Medium Quarkonia at SPS, RHIC + LHC

1. Comprehensive Analysis ofIn-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 V [½GeV] [Kaczmarek et al ‘03] r [½ fm] • Vacuum charm- + bottomonium spectroscopy well described • Non-perturbative force (EBCoul(J/y) ~ 0.05 GeVvs. 0.6 GeVexpt.) • Persists in medium to at least ~2Tc • Potential approach in medium?

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

4. 2.2 Brueckner Theory of Heavy Quarks in QGP InputProcessOutputTest quark-no. susceptibility Q → Q 0-modes lattice data spectral fcts./ eucl. correlat. - 2-body potential QQ T-matrix - QQ evolution (rate equation) Qq T-matrix Quark selfenergy exp. data Q spectra + v2 (Langevin)

5. D - D J/y reaction rate equilibrium limit (y -width) - c c J/y 3.) Transport Approach to Quarkonium Evolution [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, …] • Regeneration in QGP + HG: • detailed balance: → - ← J/y + g c + c + X • Rate • Equation: • Input from T-Matrix (weak/strong binding) Gy eBy mc*

6. 3.1 Inputs + Parameters • Input • - J/y,cc,y’, 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 ascontrols Gdiss • - incomplete c-quark equilibration: • Nyeq (t) ~ Nytherm(t) · [1-exp(-t/tceq)] q q

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

8. 3.2.2 J/y pT Spectra + Elliptic Flow at RHIC (U potential) • shallow minimum at low pT • high pT: • formation time, b feeddown, Cronin • small v2limits regeneration, • but does not exclude it [Zhao+RR ‘08]

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

10. 3.3.2 J/y at LHC: pT-Spectra + v2 • maximum at low pT confirms • expected regeneration level • room for additional regeneration • with harder pT spectra… • b-feeddown prevalent at high pT

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

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/y regeneration • - RAASPS(Ti~220) ~ RAARHIC(Ti~350) < RAALHC(Ti~550) ~ 0.5 • - low-pTenhancement of RAALHC, finite v2

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

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

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

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

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

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

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

20. 4.5 Summary of Charm Diffusion in Matter 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 • Shallow minimun around Tc ?! • Quark-Hadron Continuity?! • 20% reduction by non-perturbative HQ-gluon scattering

21. _ 3.1.3 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]

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