Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA International Conference on Strangeness in Quark Matter 2008 Tsinghua University Beijing (China), Theory and Phenomenology of Heavy Flavor at RHIC

1.) Introduction The virtue of Heavy Quarks (Q=b,c): - “large” scale m Q >>  QCD - “factorization” even at low p T - T/m Q << 1 → Brownian motion (elastic scattering) - flavor conserved in hadronization → coalescence!? Heavy Quarks as comprehensive probe: - connect p T regimes via underlying HQ interaction? - strong coupling: perturbation theory unreliable, resummations required - simpler(?) problem: heavy quarkonia ↔ potential approach - constraints for elastic heavy-quark scattering?

1.) Introduction 2.) Heavy-Quark Diffusion in QGP  Fokker-Planck Equation  Diffusion coefficients: - peturbative QCD - lattice-QCD based T-matrix - AdS/CFT 3.) Heavy-Flavor Spectra at RHIC  Bulk Evolution  Langevin Simulations + Quark Spectra  e ± Spectra and Flow 4.) Viscosity and “sQGP” 5.) Conclusions Outline

Brownian Motion: scattering rate diffusion coefficient 2.) 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 [van Hees+RR ’04]

2.2 Potential Scattering using Lattice QCD Determination of Potential fit lattice Q-Q free energy check on : no over-binding of charmonia at ~T c (+ lat-QCD correlators)  T-matrix for Q-q scatt. in QGP Casimir scaling for color chan. a G qQ : Q-q propagator [Mannarelli+RR ’05] [quench. lat-QCD, Wong ’05] [2-flavor lat-QCD, Shuryak+Zahed ’04]

2.2.2 Charm-Light QuarkT-Matrix + Drag Coefficient supports effective resonance model: S-wave mesons and diquarks up to T c,  -1 ≈ 7 fm/c P-waves and color a=6, 8 suppressed “collisional dissociation” [Adil+Vitev ‘06] ↔ vacuum potential [van Hees,Mannarelli,Greco+RR ’07] based on lattice-QCD internal energy T-Matrix Thermalization Rate

2.3 AdS/CFT-QCD Correspondence [Gubser ‘07] match energy density (d.o.f = 120 vs. ~40) and coupling constant (heavy-quark potential) to QCD 3-momentum independent  [Herzog et al, Gubser ‘06] ≈ (4-2 fm/c) -1 at T= MeV Lat-QCD T QCD ~ 250 MeV

2.4 Perturbative QCD with Running Coupling [Peshier ‘07] run QCD coupling to m D ~ gT rather than 2  T [Gossiaux+ Aichelin ‘08] factor ~10 increase in heavy-quark drag coefficient perturbative regime?

2.5 Comparison of Drag Coefficients pert. QCD with running coupling ~ AdS/CFT increase with temperature except T-matrix (melting resonances)

3.) Phenomenology at RHIC Medium evolution - hydrodynamics or parameterizations thereof - realistic bulk-v 2 (~5-6%) - stop evolution after QGP; hadronic phase? Hadronization - fragmentation: c → D + X - coalescence: c + q → D, adds momentum and v 2 - chemistry (e.g.  c enhancement) Semileptonic electron decays - approx. conserve v 2 and R AA of parent meson - charm/bottom composition in p-p [Hirano et al ’06] [Martinez et al, Sorensen et al ‘07] [Greco et al, Dong et al ‘04]

3.1 HQ Langevin Simulations: Hydro vs. Fireball Elastic pQCD + Hydrodynamics [Moore+Teaney ’05] b=6.5 fm T c =165 MeV  ≈ 9 fm/c T c =180 MeV bulk-v 2 ~5.5%  QGP ≈ 5 fm/c Resonance Model + Expanding Fireball [van Hees,Greco +RR ’05] D s (2  T) ≈ 6  v 2 max ~ 5-6% R AA ~ 0.3

3.2 Model Predictions vs. PHENIX Data Single-e ± Spectra [PHENIX ’06] coalescence increases both R AA and v 2 pQCD radiative E-loss with upscaled transport coeff. Langevin with elastic pQCD + resonances + coalescence Langevin with upscaled pQCD elastic

3.2.2 The first 5 fm/c for Charm-Quark v 2 + R AA Inclusive v 2 R AA built up earlier than v 2 Time Evolution

3.3 T-Matrix Approach vs. e ± Spectra at RHIC R AA early, v 2 “late” ↔ max. int. strength at ~T c hadronic correlations at T c ↔ quark coalescence [van Hees,Mannarelli,Greco+RR ’07]

3.4 Hydrodynamic Evolution + “AdS/CFT” Drag 10-20% central,  ~5fm/c (middle of mixed phase) [Akamatsu,Hatsuda +Hirano ’08] Further discussion: running  s, validity of FP → [P. Gossiaux, Wednesday] charm correlations → [X. Zhu, Wednesday] Charm-Quark R AA Charm-Quark v 2 ~30-50% larger v 2, R AA at b=7fm, f 0 =0 → v 2 max =4-5%  D s (2  T) ≈ 6

4.) 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

5.) Summary and Conclusions “Different” approaches to Heavy-Quark diffusion related pert-QCD  running  s  T-matrix + lQCD pot  AdS/CFT Constraints essential (e.g. HQ potential, lattice correlators) Q-q T-matrix with lQCD motivated potential: - “hadronic” correlations close to T c ↔ quark coalescence - max. int. strength at ~T c ↔ min.  /s !? gluons? U, F or …? Radiative diffusion? light-quark sector? … RHIC non-photonic e ±  D s (2  T) ≈ v 2 - R AA correlation revealing (coalescence? k t -broad.? ) - scrutinize medium evolution, Fokker-Planck, … - D/B separation, correlations, quarkonia, …

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]

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

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 

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

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

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

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

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

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