Heavy Quarks in sQGP and Observables at RHIC + LHC

1. Heavy Quarks in sQGPand Observables at RHIC + LHC Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees, D. Cabrera, X. Zhao, V. Greco, M. Mannarelli Heavy Quark Workshop Berkeley National Laboratory, 02.11.07

2. transport in QGP, hadronization 1.) Introduction: Heavy Quarks at RHIC • c, b quarks (more!?) sensitive to: • - thermalization (low pT) • - energy loss (high pT) • - coalescence (int. pT?) • Direct relation to other observables • intermediate-mass dileptons: • → e+e- X competes with thermal (QGP) radiation • quarkonia: • - interaction of c, b within bound state • - regeneration → Y What are the relevant interactions of heavy quarks at low/intermediate pT?

3. Outline 1.) Introduction  HQ Observables in URHICs 2.) Heavy Quarkonia in QGP  Charmonium Spectral + Correlation Functions  Lattice-QCD based Potential Approach (T-Matrix!)  Suppression vs. Regeneration at RHIC 3.) Open Heavy Flavor in QGP  Heavy-Light Quark T-Matrix  HQ Selfenergies + Transport Coefficients  HQ and e± Spectra 4.)Conclusions

4. accurate lattice “data” forEuclidean Correlator hc cc [Datta et al ‘04] • S-wave charmonia little changed to ~2Tc • similar in other lQCD studies[Iida et al ’06, Jakovac et al ’07, Aarts et al ’07] 2.1 Quarkonia in Lattice QCD • direct computation of • Euclidean Correlation Fct. spectral function

5. - 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 ’06, Mocsy+Petreczky ’06] Y’ cont. w 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

6. 2.2.2 Uncertainty I: “Lattice QCD-based” Potentials • accurate lattice “data” forfree energy:F1(r,T) = U1(r,T) – T S1(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]

7. 2.3 Charmonium Spectral Functions in QGP withinT-Matrix Approach (lattice U1 Potential) Fixedmc=1.7GeV In-mediummc* (U1subtraction) hc hc • gradual decrease of binding, rescattering enhancement! • hc , J/y survive until ~2.5Tc , ccup to ~1.2Tc

8. 2.4.1 Charmonium Correlators I: S-Waves • lattice U1-potential, in-medium mc* [Cabrera+RR in prep] T-Matrix Approach [Aarts et al. ‘07] Lattice QCD J/y hc • fair agreement!

9. 2.4.2 Charmonium Correlators II: P-Waves • lattice U1-potential, in-medium mc* [Cabrera +RR in prep] T-Matrix Approach [Aarts et al. ‘07] Lattice QCD cc0 cc1 • fair agreement!

10. 2.5 Observables at RHIC: Centrality + pT Spectra • update of ’03 predictions: - 3-momentum dependence • - less nucl. absorption + c-quark thermalization [X.Zhao+RR in prep] • direct ≈ regenerated (cf. ) • sensitive to: tctherm , mc* , Ncc [Yan et al. ‘06]

11. _ _ q q Microscopic Calculations of Diffusion: q,g c • pQCD elastic scattering:g-1= ttherm ≥20 fm/cslow [Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04] • D-/B-resonance model:g-1= ttherm ~ 5 fm/c “D” parameters: mD , GD c c • new development: lQCD-potential scattering (no parameter) [van Hees et al. ’07] 3.) Heavy Quarks in the QGP • Brownian • Motion: Fokker Planck Eq. [Svetitsky ’88,…] Q scattering rate diffusion constant

12. coalescence essential for • consistent RAA and v2 • other mechanisms: • 3-body collisions, … [Liu+Ko’06, Adil+Vitev ‘06] 3.2 Model Comparisons to Recent PHENIX Data Single-e±Spectra [PHENIX ’06] • pQCD radiative E-loss with • 10-fold upscaled transport coeff. • Langevin with elastic pQCD + • resonances + coalescence • Langevin with 2-6 upscaled • pQCD elastic

13. 3.2.2 Transport Properties of (s)QGP ‹x2›-‹x›2 ~ Ds·t , Ds ~ 1/g Spatial Diffusion Coefficient: Charm-Quark Diffusion Viscosity-to-Entropy: Lattice QCD [Nakamura +Sakai ’04] • small spatial diffusion → strong coupling • E.g. AdS/CFT correspondence:h/s=1/4p, DHQ≈1/2pT •  resonances: DHQ≈4-6/2pT , DHQ ~ h/s ≈ (1-1.5)/p

14. 3.3 Potential Scattering in sQGP Q-qT-Matrix • T-matrix for Q-q scatt. in QGP • solve numerically given VQq (p,p’) • Casimir scaling for color channels a [Mannarelli+RR ’05] • determination of potential • -fit latticeQ-Qfree energy • - Fourier transfo. + • partial-wave exp. • - relativist. correc. • for finite mQ,q • still significant • uncertainty _ [Shuryak+ Zahed ’04] [Wong ’05]

15. 3.3.2 Charm-Light T-Matrix with lQCD-based Potential Temperature Evolution + Channel Decomposition [van Hees, Mannarelli, Greco+RR ’07] • meson and diquarkS-wave resonances up to 1.2-1.5Tc • P-waves and (repulsive) color-6, -8 channels suppressed

16. 3.3.3 Charm-Quark Selfenergy + Transport Selfenergy Friction Coefficient • charm quark widths Gc = -2 ImSc~ 200MeV close to Tc • friction coefficients decrease(!) with increasing T !

17. 3.4 Maximal “Interaction Strength” in the sQGP • potential-based description ↔ strongest interactions close to Tc • consistent with minimum in h/s at ~Tc • cf. bottom-up (hadron gas) + top-down (pQCD) extrapolations • strong hadronic correlations at Tc • ↔ quark coalescence! [Kapusta ’06]

18. 3.5.1 Charm-Quark Spectra at RHIC • relativistic Langevin simulation in thermal fireball background Elliptic Flow Nuclear Suppression Factor • importance of nonperturbative effects supported • radiative (2↔3) scattering?

19. 3.5.2 Single-Electron Spectra at RHIC

20. 3.6 Heavy-Quark + Single-e± Spectra at LHC • relativistic Langevin simulation in thermal fireball background • resonances inoperative at T>2Tc , coalescence at Tc • harder input spectra, slightly more suppression  RAA similar to RHIC

21. 4.) Summary and Conclusions • T-matrix approach with lQCD internal energy (UQQ): • S-wave charmonia survive up to ~2.5Tc, • supported by lQCD correlators + spectral functions • T-matrix approach for heavy-light scattering: • large c-quark width + small diffusion (elastic, nonperturbative) • “Hadronic” correlations dominant (meson + diquark) • - maximum strength close to Tc ↔ minimum in h/s !? • - naturally merge into quark coalescence at Tc[Ravagli+RR ’07] • Observables: quarkonia, HQ suppression+flow, dileptons,… • Consequences for light-quark sector? Potential approach?

22. 3.5.2 The first 5 fm/c for Charm-Quark v2 + RAA Inclusive v2 • RAA built up earlier than v2

23. 2.3.3 HQ Langevin Simulations: Hydro vs. Fireball Elastic pQCD (charm) + Hydrodynamics [Moore+Teaney ’04] as , g 1 , 3.5 0.5 , 2.5 0.25,1.8 • Tc=165MeV, • t ≈ 9fm/c • sgQ ~ (as/mD)2 • as and mD~gT • independent • (mD≡1.5T) • as=0.4, mD=2.2T • ↔ D(2pT) ≈ 20 •  hydro ≈ • fireball • expansion [van Hees,Greco+RR ’05]

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

25. 2.4.2 Single-e± at RHIC: Resonances + Q-q Coalescence fqfrom p, K [Greco et al ’03] Elliptic Flow Nuclear Modification Factor • less suppression and morev2 • anti-correlation RAA ↔ v2 from coalescence (both up) • radiative E-loss at high pT?!

26. Nuclear Modification Factor Elliptic Flow • resonances → large charm suppression+collectivity, not for bottom • v2 “leveling off ” characteristic for transition thermal → kinetic 2.3 Heavy-Quark Spectra at RHIC • Relativistic Langevin Simulation: • stochastic implementation of HQ motion in expanding QGP-fireball • “hydrodynamic” evolution of bulk-matterbT , v2 [van Hees,Greco+RR ’05]

27. 2.1.3 Thermal Relaxation of Heavy Quarks in QGP Charm: pQCD vs. Resonances Charm vs. Bottom pQCD “D” • tctherm ≈ tQGP ≈ 3-5 fm/c • bottom does not thermalize • factor ~3 faster with • resonance interactions!

28. 5.3.2 Dileptons II: RHIC [R. Averbeck, PHENIX] [RR ’01] QGP • low mass: thermal! (mostly in-medium r) • connection to Chiral Restoration: a1 (1260)→ pg ,3p • int. mass:QGP (resonances?)vs.cc → e+e-X (softening?) -