1. Heavy Flavor in the sQGP Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees, D. Cabrera (Madrid), X. Zhao, V. Greco (Catania), M. Mannarelli (Barcelona) 24. Winter Workshop on Nuclear Dynamics South Padre Island (Texas), 09.04.08

2. 1.) Introduction Empirical evidence for sQGP at RHIC: - thermalization / low viscosity (low p T ) - energy loss / large opacity (high p T ) - quark coalescence (intermed. p T ) Heavy Quarks as comprehensive probe: - connect p T regimes via underlying HQ interaction? - strong coupling: perturbation theory becomes unreliable, resummations required - simpler(?) problem: heavy quarkonia ↔ potential approach - similar interactions operative for elastic heavy-quark scattering? transport in QGP, hadronization

3. 1.) Introduction 2.) Heavy Quarkonia in QGP  Charmonium Spectral + Correlation Functions  In-Medium T-Matrix with “lattice-QCD” potential 3.) Open Heavy Flavor in QGP  Heavy-Light Quark T-Matrix  HQ Selfenergies + Transport  HQ and e ± Spectra  Implications for sQGP 4.) Constituent-Quark Number Scaling 5.) Conclusions Outline

4. 2.1 Quarkonia in Lattice QCD accurate lattice “data” for Euclidean Correlator S-wave charmonia little changed to ~2T c [Iida et al ’06, Jakovac et al ’07, Aarts et al ’07] cc cc [Datta et al ‘04] direct computation of Euclidean Correlation Fct. spectral function

5. Correlator: L=S,P Lippmann-Schwinger Equation In-Medium Q-Q T-Matrix: - 2.2 Potential-Model Approaches for Spectral Fcts. [Mannarelli+RR ’05,Cabrera+RR ‘06] - 2-quasi-particle propagator: - bound+scatt. states, nonperturbative threshold effects (large) bound state + free continuum model too schematic for broad / dissolving states  2  J/  ’’ cont. E thr [Karsch et al. ’87, …, Wong et al. ’05, Mocsy+Petreczky ‘06, Alberico et al. ‘06, …]

6. 2.2.2 “Lattice QCD-based” Potentials accurate lattice “data” for free energy: F 1 (r,T) = U 1 (r,T) – T S 1 (r,T) V 1 (r,T) ≡ U 1 (r,T)  U 1 (r=∞,T) [Cabrera+RR ’06; Petreczky+Petrov’04] [Wong ’05; Kaczmarek et al ‘03] (much) smaller binding for V 1 =F 1, V 1 = (1-  U 1 +  F 1

7. 2.3 Charmonium Spectral Functions in QGP within T-Matrix Approach (lattice U 1 Potential ) In-medium m c * (U 1 subtraction) cc gradual decrease of binding, large rescattering enhancement  c, J/  survive until ~2.5T c,  c up to ~1.2T c cc Fixed m c =1.7GeV

8. 2.4 Charmonium Correlators above T c lattice U 1 -potential, in-medium m c *, zero-mode G zero ~ T  (T) cc T-Matrix Approach Lattice QCD [Cabrera+RR in prep.] [Aarts et al. ‘07] qualitative agreement  c1

9. Brownian Motion: scattering rate diffusion constant 3.) Heavy Quarks in the QGP Fokker Planck Eq. [Svetitsky ’88,…] Q pQCD elastic scattering:  -1  =  therm ≥20 fm/c slow q,g c Microscopic Calculations of Diffusion: [Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04] D-/B-resonance model:  -1  =  therm ~ 5 fm/c c “D” c _ q _ q parameters: m D, G D recent development: lQCD-potential scattering [van Hees, Mannarelli, Greco+RR ’07]

10. 3.2 Potential Scattering in sQGP Determination of potential fit lattice Q-Q free energy currently significant uncertainty  T-matrix for Q-q scatt. in QGP Casimir scaling for color chan. a in-medium heavy-quark selfenergy: [Mannarelli+RR ’05] [Wong ’05] [Shuryak+ Zahed ’04]

11. 3.2.2 Charm-Light T-Matrix with lQCD-based Potential meson and diquark S-wave resonances up to 1.2-1.5T c P-waves and (repulsive) color-6, -8 channels suppressed [van Hees, Mannarelli, Greco+RR ’07] Temperature Evolution + Channel Decomposition

12. 3.2.3 Charm-Quark Selfenergy + Transport charm quark widths  c = -2 Im  c ~ 250MeV close to T c friction coefficients increase(!) with decreasing T→ T c ! Selfenergy Friction Coefficient

13. 3.3 Heavy-Quark Spectra at RHIC T-matrix approach ≈ effective resonance model other mechanisms: radiative (2↔3), … relativistic Langevin simulation in thermal fireball background p T [GeV] Nuclear Modification Factor Elliptic Flow p T [GeV] [Wiedemann et al.’05,Wicks et al.’06, Vitev et al.’06, Ko et al.’06]

14. 3.5 Single-Electron Spectra at RHIC heavy-quark hadronization: coalescence at T c [Greco et al. ’04] + fragmentation hadronic correlations at T c ↔ quark coalescence! charm bottom crossing at p T e ~ 5GeV in d-Au (~3.5GeV in Au-Au) ~30% uncertainty due to lattice QCD potential suppression “early”, v 2 “late”

15. 3.6 Maximal “Interaction Strength” in the sQGP potential-based description ↔ strongest interactions close to T c - consistent with minimum in  /s at ~T c - strong hadronic correlations at T c ↔ quark coalescence semi-quantitative estimate for diffusion constant: [Lacey et al. ’06] weak coupl.  s ≈  n tr =1/5 T D s strong coupl.  s  ≈  D s  = 1/2 T D s   s  ≈  close to  T c

16. 4.) Constitutent-Quark Number Scaling of v 2 CQNS difficult to recover with local v 2,q (p,r) “Resonance Recombination Model”: resonance scatt. q+q → M close to T c using Boltzmann eq. quark phase-space distrib. from relativistic Langevin, hadronization at T c : [Ravagli+RR ’07] [Molnar ’04, Greco+Ko ’05, Pratt+Pal ‘05] energy conservation thermal equil. limit interaction strength adjusted to v 2 max ≈ 7% no fragmentation K T scaling at both quark and meson level 

17. 5.) Summary and Conclusions T-matrix approach with lQCD internal energy (U QQ ): S-wave charmonia survive up to ~2.5T c, consistent with lQCD correlators + spectral functions T-matrix approach for (elastic) heavy-light scattering: large c-quark width + small diffusion “Hadronic” correlations dominant (meson + diquark) - maximum strength close to T c ↔ minimum in  /s !? - naturally merge into quark coalescence at T c Observables: quarkonia, HQ suppression+flow, dileptons,… Consequences for light-quark sector? Radiative processes? Potential approach?

18. 3.5.2 The first 5 fm/c for Charm-Quark v 2 + R AA Inclusive v 2 R AA built up earlier than v 2

19. 3.2.4 Temperature Dependence of Charm-Quark Mass significant deviation only close to T c

20. 2.3.3 HQ Langevin Simulations: Hydro vs. Fireball [van Hees,Greco+RR ’05] Elastic pQCD (charm) + Hydrodynamics  s, g 1, 3.5 0.5, 2.5 0.25,1.8 [Moore+Teaney ’04] T c =165MeV,  ≈ 9fm/c  gQ ~ (  s /  D ) 2  s and  D ~gT independent (  D ≡1.5T)  s =0.4,  D =2.2T ↔ D(2  T) ≈ 20  hydro ≈ fireball expansion

21. 3.6 Heavy-Quark + Single-e ± Spectra at LHC harder input spectra, slightly more suppression  R AA similar to RHIC relativistic Langevin simulation in thermal fireball background resonances inoperative at T>2T c, coalescence at T c

22. direct ≈ regenerated (cf. ) sensitive to:  c therm, m c *, N cc 2.5 Observables at RHIC: Centrality + p T Spectra [X.Zhao+RR in prep] [Yan et al. ‘06] update of ’03 predictions: - 3-momentum dependence - less nucl. absorption + c-quark thermalization

23. 3.2 Model Comparisons to Recent PHENIX Data Single-e ± Spectra [PHENIX ’06] coalescence essential for consistent R AA and v 2 other mechanisms: 3-body collisions, … [Liu+Ko’06, Adil+Vitev ‘06] pQCD radiative E-loss with 10-fold upscaled transport coeff. Langevin with elastic pQCD + resonances + coalescence Langevin with 2-6 upscaled pQCD elastic

24. 3.2.2 Transport Properties of (s)QGP small spatial diffusion → strong coupling Spatial Diffusion Coefficient: ‹x 2 ›-‹x› 2 ~ D s ·t, D s ~ 1/  E.g. AdS/CFT correspondence:  /s=1/4 , D HQ ≈1/2  T  resonances: D HQ ≈4-6/2  T, D HQ ~  /s ≈ (1-1.5)/  Charm-Quark Diffusion Viscosity-to-Entropy: Lattice QCD [Nakamura +Sakai ’04]

25. 2.4 Single-e ± at RHIC: Effect of Resonances hadronize output from Langevin HQs (  -fct. fragmentation, coalescence) semileptonic decays: D, B → e+ +X large suppression from resonances, elliptic flow underpredicted (?) bottom sets in at p T ~2.5GeV Fragmentation only

26. less suppression and more v 2 anti-correlation R AA ↔ v 2 from coalescence (both up) radiative E-loss at high p T ?! 2.4.2 Single-e ± at RHIC: Resonances + Q-q Coalescence f q from , K Nuclear Modification Factor Elliptic Flow [Greco et al ’03]

27. Relativistic Langevin Simulation: stochastic implementation of HQ motion in expanding QGP-fireball “hydrodynamic” evolution of bulk-matter  T, v 2 2.3 Heavy-Quark Spectra at RHIC [van Hees,Greco+RR ’05] Nuclear Modification Factor resonances → large charm suppression+collectivity, not for bottom v 2 “leveling off ” characteristic for transition thermal → kinetic Elliptic Flow

28. 2.1.3 Thermal Relaxation of Heavy Quarks in QGP factor ~3 faster with resonance interactions! Charm: pQCD vs. Resonances pQCD “D”  c therm ≈  QGP ≈ 3-5 fm/c bottom does not thermalize Charm vs. Bottom

29. 5.3.2 Dileptons II: RHIC low mass: thermal! (mostly in-medium  ) connection to Chiral Restoration: a 1 (1260)→ , 3  int. mass: QGP (resonances?) vs. cc → e + e - X (softening?) - [RR ’01] [R. Averbeck, PHENIX] QGP