Nonperturbative Heavy-Quark Transport at RHIC

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) 417th WE-Heraeus Seminar on “Characterization of the QGP with Heavy Quarks” Physikzentrum Bad Honnef, 28.06.08

2. transport in QGP, hadronization Run-7 Run-4 1.) Introduction • Empirical evidence for sQGP at RHIC: • - thermalization / low viscosity (low pT) • - energy loss / large opacity (high pT) • - quark coalescence (intermed. pT) • Heavy Quarks as comprehensive probe: • - pT 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? PRELIMINARY minimum-bias resonance model [van Hees, Greco+RR ’05]

3. Outline 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

4. 2.) Quarkonia in QGP: Potential Models J/y [Karsch et al. ’87, …, Shuryak+Zahed ’04, Mocsy+Petreczky‘05, Alberico et al. ‘06, Wong et al. ’07, Laine et al. ‘07 …] s/w2 Y’ • bound state + (free) continuum model • too schematic for broad/dissolving states cont. w Ethr • Lippmann-Schwinger Equation [Mannarelli+RR ’05, Cabrera+RR ‘06] In-Medium Q-QT-Matrix: - - quasi-particle propagator: - bound+scatt. states, threshold effects large • Correlator: L=S,P

5. 2.2 “Lattice QCD-based” Potentials • free energy: F1(r,T) = U1(r,T) – T S1(r,T) - potential? • V1(r,T) ≡ U1(r,T) - U1(r=∞,T) or V1=F1, V1 = a F1 +(1-a) U1  (much) smaller binding: [Cabrera+RR ’06; Petreczky+Petrov’04] [Wong ’05; Kaczmarek et al ‘03]

6. 2.3 Charmonium Spectral Functions in QGP • T-Matrix Approach with V1=U1 In-mediummc* (U1subtraction) Fixedmc=1.7GeV, Gc=20MeV hc hc • screening reduces binding; large rescattering enhancement • hc mass stabilized by decreasing mc*: my = 2mc* -eB • hc “survives” up to ~2.5Tc (ccup to ~1.2Tc)

7. 2.4 Charmonium Correlators in QGP Lattice QCD [Cabrera +RR ‘06] T-Matrix with U1 hc [Aarts et al. ‘07] hc [Datta et al ‘04] • in-medium mc* compensates • reduced binding: my = 2mc* - eB

8. _ 2.5 Finite-Width Effects • c-quark width in propagator • dominant process depends on eB J/y Lifetime [Bhanot+Peskin ’79] [Grandchamp+RR ‘01] • effect on correlator (mc=1.7GeV) • increasing width further • stabilizes correlators • note:GY = 100 MeV • ~60%J/ydestroyed inDt=2fm/c hc [Cabrera+RR ‘06]

9. _ _ 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, Gossiaux et al. ’05, …] • D-/B-resonance model:g-1= ttherm ~ 5 fm/c “D” parameters: mD , GD c c • recent development: “latt.-QCD potential” scattering [van Hees, Mannarelli, Greco+RR ’07] 3.) Heavy Quarks in the QGP • Brownian • Motion: Fokker Planck Eq. [Svetitsky ’88,…] Q scattering rate diffusion constant

10. 3.2 Potential Scattering in sQGP [Mannarelli+RR ’05] • T-matrix for Q-q scatt. in QGP • Casimir scaling for color chan. a • in-medium heavy-quark selfenergy: • Determination of potential • fit latticeQ-Qfree energy • currently • significant • uncertainty • augment by • magnetic • interaction _ Nf=2 [Shuryak+ Zahed ’04] Nf=0 [Wong ’05]

11. 3.2.2 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

12. 3.2.3 Charm-Quark Selfenergy + Transport Selfenergy Friction Coefficient • large charm-quark width • Gc = -2 ImSc ~ 250MeV close to Tc • friction coefficients increase(!) • with decreasing T→Tc!

13. 3.3 Heavy-Quark Spectra at RHIC • relativistic Langevin simulation in thermal fireball background Nuclear Modification Factor Elliptic Flow pT [GeV] pT [GeV] • T-matrix approach ≈ effective resonance model • other mechanisms: radiative (2↔3), … [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 Tc [Greco et al. ’04] • + fragmentation • hadronic correlations at Tc • ↔ quark coalescence! • charm bottom crossing • at pTe ~ 5GeV in d-Au • (~3.5GeV in Au-Au) • ~25% uncertainty due to • differences in U1 potential • suppression “early”, v2 “late”

15. 3.5 Maximal “Interaction Strength” in the sQGP • potential-based description ↔ strongest interactions close to Tc • - minimum in h/s at ~Tc • - hadronic correlations at Tc ↔ quark coalescence • estimate diffusion constant: weak coupl. h/s ≈ 4/15 n <p> ltr=1/5 T Ds strong coupl. h/s≈ 1/4p Ds(2pT) = 1/2 T Ds  h/s≈ (2-4)/4p close toTc [Lacey et al. ’06] [RR+ van Hees ’08]

16. 4.) Summary and Conclusions • T-matrix approach with lQCD internal energy (UQQ): • - S-wave charmonia survive up to Tdiss≤2.5Tc • - finite width can suppress J/y well below Tdiss! • T-matrix for (elastic) heavy-light scattering: • - large c-quark width + small diffusion • - “hadronic” correlations dominant (meson + diquark) • - maximum strength close to Tc ↔ minimum in h/s ? • - naturally merges into quark coalescence at Tc • 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 v2 + RAA Inclusive v2 • RAA built up earlier than v2

18. 4.) Constitutent-Quark Number Scaling of v2 [Molnar ’04, Greco+Ko ’05, Pratt+Pal ‘05] • CQNS difficult to recover withlocalv2,q(p,r) • “Resonance Recombination Model”: • resonance scatt. q+q → M close to Tc using Boltzmann eq. • quark phase-space distrib. from relativistic Langevin, hadronization at Tc: - [Ravagli+RR ’07] • energy conservation • thermal equil. limit • interaction strength • adjusted to v2max ≈7% • no fragmentation • KT scaling at both • quark and meson level

19. 2.2.3 In-Medium Charm-Quark Mass [Kaczmarek+Zantow ’05] • significant deviation only close to Tc • cf. also [Petreczky QM ‘08]

20. 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]

21. 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

22. 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]

23. 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

24. 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

25. 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

26. 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?!

27. 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]

28. 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!

29. 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?) -