1. Heavy-Quark Thermalization and Resonances in the QGP Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees (Texas A&M), V. Greco (Texas A&M, Catania) Quark Matter 2005 Conference Budapest (Hungary), 06.08.05

2. 1.) Introduction: Single-e ± Spectra pre-QM05 Coalescence assuming v 2 (c) = v 2 (q) and/or jet quenching? dynamical origin of strong re-interactions consistency v 2 ↔ R AA open-bottom “contamination” induced radiation vs. elastic scattering … Challenges: p T [GeV/c] R AA Djordjevic etal. ‘04 Armesto etal.‘05 jet-quench [Djordjevic etal ’04]

3. 2.) Baseline Spectra in p-p, d-Au  Charm vs. Bottom 3.) Heavy-Quark Elastic Scattering in QGP  pQCD vs. Resonances  Brownian Motion and Thermal Relaxation 4.) Heavy-Quark and Electron Spectra at RHIC  Langevin Simulation, Hadronization  R AA and v 2 5.) Heavy Quarkonia  Charmonium p T -Spectra 6.) Conclusions Outline

4. 2.) Heavy-Flavor Baseline Spectra at RHIC Single-Electron Decays D-Mesons bottom crossing at 5GeV !? (pQCD: ~4GeV [Cacciari etal ’05] ) strategy: fix charm with D-mesons, adjust bottom in e ± -spectra

5. Brownian Motion: scatt. rate diff. const. 3.) Elastic Heavy-Quark Scattering in the QGP e.g. T=400MeV,  s =0.4   = 0.1 fm -1 ↔  therm ~10fm/c slow! 3.1 Perturbative QCD gcgc qcqc dominated by t-channel gluon-ex in gc→gc: Fokker Planck Eq. [Svetitsky ’88, Mustafa etal ’98, Molnar etal ’04 Zhang etal. ’04, Teaney+Moore‘04]

6. 3.2 Open-Charm Resonances in QGP effective model with pseudo/scalar + axial/vector “D-mesons” “Light”-Quark Resonances 1.4T c [Asakawa+ Hatsuda ’03] parameters: m D (0) =2GeV, G D, m c =1.5GeV, m q =0 number of D-states: 4 per u and d, 2 for s cross section isotropic more microscopic → [M.Mannarelli’s talk] [van Hees+ RR ’04] c “D” c _ q _ q

7. 3.3 Heavy-Quark Thermalization Times in QGP substantially smaller for resonances Charm: pQCD vs. Resonances pQCD “D”  c relax ≥  (T>0.25GeV) ≈ 1fm/c bottom does not thermalize (10%) Charm vs. Bottom

8. → stochastic implementation of heavy quarks in expanding fireball with realistic time evolution of bulk v 0, v 2 4.) Heavy-Quark and Electron Spectra at RHIC 4.1 Relativistic Langevin Simulations [van Hees,Greco+RR ’05] Nuclear Suppression Factor pQCD elastic scatt. moderate resonance effects substantial characteristic “leveling-off” factor ~4 from resonances Elliptic Flow

9. 4.2 Single-Electron v 2 and R AA at RHIC f q from , K coalescence + fragment. [van Hees, Greco +RR ’05] coalescence increases both R AA and v 2, resonances essential bottom contribution reduces effects induced gluon radiation? Elliptic Flow Nuclear Suppression Factor Minimun-Bias Au-Au 200GeV Minimun-Bias Au-Au 200GeV

10. 5.) J/  p t -Spectra in Au-Au at RHIC total yields different by factor 3 large sensitivity to radial flow (  t,max =0.5-0.65) [Thews+Mangano ’05] [Greco,Ko+RR ’04] Quark Coalescence at T c

11. 6.) Summary “D”-meson resonances in QGP (lQCD spectral fcts., potentials)  c(b)-quark thermalization ~4(12)fm/c (elastic scattering), (factor ~3 faster than pQCD) Langevin simulation for RHIC + coalescence/fragmentation: - electrons: v 2 ≤ 11%, R AA ≥ 0.45 (MinBias), “compromised” by bottom - predictions similar to new PHENIX data sQGP elastic scattering (resonances) prevalent over radiation at low / medium p t !? (more) uncertainties: hadronic phase (lifetime), smaller m c (?), bottom contribution, softer fragmentation impact on quarkonia, dileptons (intermediate mass)

12. 3.) Resonances in QGP: Microscopic Description Lattice Q-Q Free Energy [Bielefeld Group ’04] Applications → Schröd.-Eq. → bound states (sQGP)! scattering states? imaginary parts? → Lippmann-Schwinger Equation [Shuryak,Zahed, Brown ’04]  Selfconsistency Problem [Mannarelli+RR ’05] q-q T-Matrix - Quark- Selfenergy

13. 3.2 Selfconsistent T-Matrix and Selfenergy [Mannarelli+RR ’05] assume m q (gluon)=0.1GeV transition from bound (1.2T c ) to resonance states! quark-width ≈0.3GeV ≈ (2/3fm) -1 (≈ mass ↔ liquid!?) colored states, equat. of state? q-q T-Matrices - Quark Self- Energy T=1.2T c T=1.5T c T=1.75T c T=1.5T c

14. Individual Charm- and Bottom-Electron R AA and v 2

15. 2.4.2 Langevin-Simul. at RHIC: Heavy-Quark v 2 Resonances vs. pQCD Charm-pQCD (  s,  D =1.5T) [van Hees,Greco+RR ’05] characteristic “leveling-off” factor ~4 from resonances more sensitive to res.-coupling hydro with T c =165,  ≈ 9fm/c  s and Debye mass independent [Moore and Teaney ’04]

16. 2.4.1 Langevin-Simul. at RHIC: Heavy-Quark R AA [van Hees,Greco+RR ’05] Resonances vs. pQCD Charm-pQCD (  s,  D =1.5T)  s, g 1, 3.5 0.5, 2.5 0.25,1.8 [Moore and Teaney ’04] hydro with T c =165MeV,  ≈ 9fm/c  s and Debye mass independent expanding fireball ≈ hydro pQCD elastic scatt. moderate resonance effects substantial

17. c-Quark Drag and Diffusion Coefficients in QGP substantially smaller for resonances Thermalization Times [van Hees+RR ’04] pQCD “D” Coordinate Space Diffusion ‹x 2 › - ‹x› 2 = D x t ≈ (5 fm) 2 ~ fireball size at T c

18. QGP-suppression prevalent no “jump” in theory QGP-regeneration dominant sensitive to: m c *, (N cc ) 2 ↔ rapidity, √s, A 4.4 Charmonium in A-A SPS RHIC [Grandchamp etal. ’03] Pb(158AGeV)-Pb [Grandchamp +RR ’03] J/  Excitation Function same net suppression at SPS + RHIC!

19. 3.4.3 Scrutinizing Charmonium Regeneration II: J/  Elliptic Flow Suppression only Thermal Coalescence at T c [Wang+Yuan ’02] [Greco etal ’04] MB Au-Au factor ~5 different! transition in p t !?