1. Nonperturbative Heavy-Quark Transport at RHIC Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees (Giessen), D. Cabrera (Madrid), V. Greco (Catania), M. Mannarelli (Barcelona) 417 th WE-Heraeus Seminar on “Characterization of the QGP with Heavy Quarks” Physikzentrum Bad Honnef, 28.06.08

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: - p T regimes connected via underlying HQ interaction? - strong coupling: perturbation theory unreliable, resummations required - simpler(?) problem: heavy quarkonia ↔ potential approach - similar interactions operative for elastic heavy-quark scattering? transport in QGP, hadronization PRELIMINARY Run-4 Run-7 resonance model [van Hees, Greco+RR ’05] minimum-bias

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

4. Correlator: L=S,P Lippmann-Schwinger Equation In-Medium Q-Q T-Matrix: - 2.) Quarkonia in QGP: Potential Models [Mannarelli+RR ’05, Cabrera+RR ‘06] - quasi-particle propagator: - bound+scatt. states, threshold effects large bound state + (free) continuum model too schematic for broad/dissolving states  2  J/  ’’ cont. E thr [Karsch et al. ’87, …, Shuryak+Zahed ’04, Mocsy+Petreczky‘05, Alberico et al. ‘06, Wong et al. ’07, Laine et al. ‘07 …]

5. 2.2 “Lattice QCD-based” Potentials free energy: F 1 (r,T) = U 1 (r,T) – T S 1 (r,T)  potential? V 1 (r,T) ≡ U 1 (r,T)  U 1 (r=∞,T) or [Cabrera+RR ’06; Petreczky+Petrov’04] [Wong ’05; Kaczmarek et al ‘03] V 1 =F 1, V 1 =  F 1 +  (1-  U 1  (much) smaller binding:

6. 2.3 Charmonium Spectral Functions in QGP In-medium m c * (U 1 subtraction) cc screening reduces binding; large rescattering enhancement  c mass stabilized by decreasing m c *: m  = 2m c *   B  c “survives” up to ~2.5T c (  c up to ~1.2T c ) cc Fixed m c =1.7GeV,  c =20MeV T-Matrix Approach with V 1 =U 1

7. 2.4 Charmonium Correlators in QGP in-medium m c * compensates reduced binding: m  = 2m c * -  B cc T-Matrix with U 1 Lattice QCD [Cabrera +RR ‘06] cc [Datta et al ‘04] [Aarts et al. ‘07]

8. 2.5 Finite-Width Effects c-quark width in propagator dominant process depends on  B J/  Lifetime _ [Grandchamp+RR ‘01] increasing width further stabilizes correlators note:   = 100 MeV  ~60% J/  destroyed in  =2fm/c effect on correlator (m c =1.7GeV) cc [Bhanot+Peskin ’79] [Cabrera+RR ‘06]

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, Gossiaux et al. ’05, …] D-/B-resonance model:  -1  =  therm ~ 5 fm/c c “D” c _ q _ q parameters: m D, G D recent development: “latt.-QCD 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 augment by magnetic interaction  T-matrix for Q-q scatt. in QGP Casimir scaling for color chan. a in-medium heavy-quark selfenergy: [Mannarelli+RR ’05] N f =0 [Wong ’05] N f =2 [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 large charm-quark width  c = -2 Im  c ~ 250MeV close to T c Selfenergy Friction Coefficient friction coefficients increase(!) with decreasing T→ T c !

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. 3.4 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) ~25% uncertainty due to differences in U 1 potential suppression “early”, v 2 “late”

15. 3.5 Maximal “Interaction Strength” in the sQGP potential-based description ↔ strongest interactions close to T c - minimum in  /s at ~T c - hadronic correlations at T c ↔ quark coalescence estimate 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 [RR+ van Hees ’08]

16. 4.) Summary and Conclusions T-matrix approach with lQCD internal energy (U QQ ): - S-wave charmonia survive up to T diss ≤ 2.5T c - finite width can suppress J/  well below T diss ! T-matrix 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 merges into quark coalescence at T c Open problems + challenges: - potential approach/definition, heavy-quark masses - radiative processes, light-quark sector - observables (open charm/bottom, quarkonia, dileptons,…)

17. 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

18. 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 

19. 2.2.3 In-Medium Charm-Quark Mass significant deviation only close to T c cf. also [Petreczky QM ‘08] [Kaczmarek+Zantow ’05]

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