Heavy Quark Diffusion in Heavy Ion Collisions Ralf

Heavy Quark Diffusion in Heavy Ion Collisions Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees, V. Greco, M. Mannarelli Conference on “Early Time Dynamics in Heavy Ion Collisions” Mc. Gill University (Montreal, Canada), 16. 07

1. ) Introduction: Heavy Quarks at RHIC • c, b quarks (more!? ) sensitive to: Diffusion/interactions - thermalization (low p. T) in s. QGP at all p. T - energy loss (high p. T) Hadronization (low p. T? ) - coalescence (int. p. T? ) Direct relation to other observables • quarkonia: - interaction with c, b within bound state - regeneration →Y • intermediate-mass dileptons: → e+e- X competes with thermal (QGP) radiation [PHENIX ’ 07]

Outline 1. ) Introduction Single-Electron Puzzle at RHIC 2. ) Heavy-Quark Diffusion in (s)QGP Fokker-Planck Approach Resonance Model HQ and e± Spectra at RHIC 3. ) Lattice-QCD Based Potential Approach In-Medium Heavy-Light Quark T-Matrix Transport Coefficients HQ RAA and v 2 4. ) Conclusions

1. 2 Expectations at RHIC c, b • Radiative energy loss smaller for c+b quarks • Elastic interactions? • Collective flow? Heavy-quark diffusion? • experimental tool: electron spectra D, B → e. X RAA = (AA) / (pp) Nuclear Modification Factor Elliptic Flow [Gyulassy etal ’ 05] ? [Armesto et al ’ 05] p. T [Ge. V] • factor 4 -5 suppression • elastic E-loss, p. QCD? ! • substantial collectivity • bottom “contamination”?

2. ) Heavy-Quark Diffusion in the QGP Q • Brownian Motion: scattering rate Fokker Planck Eq. [Svetitsky ’ 88, …] diffusion constant Microscopic Calculations of Diffusion: [Svetitsky ’ 88, Mustafa et al ’ 98, Molnar et al ’ 04, Zhang et al ’ 04, Hees+RR ’ 04, Teaney+Moore‘ 04] 2. 1. 1 Perturbative QCD g q c c dominated by t-channel gluon-ex. : • e. g. T =300 Me. V, as=0. 4: ttherm~15 fm/c slow! (t. QGP ≤ 5 fm/c)

2. 1. 2 Open-Charm Resonances in QGP _ q c _ “D” q c “Light”-Quark Resonances [van Hees+ RR ’ 04] • effective lagrangian with pseudo/scalar + axial/vector “D-mesons” • parameters: m. D=2 Ge. V , GD , mc=1. 5 Ge. V, mq=0 • chiral (u, d) + HQ (c, b) symmetry • resonance cross section isotropic, p. QCD forward 1. 4 Tc [Asakawa+ Hatsuda ’ 03]

2. 1. 3 Thermal Relaxation of Heavy Quarks in QGP Charm: p. QCD vs. Resonances Charm vs. Bottom p. QCD “D” • factor ~3 faster with resonance interactions! • tctherm ≈ t. QGP ≈ 3 -5 fm/c • bottom does not thermalize

2. 3 Heavy-Quark Spectra at RHIC [van Hees, Greco+RR ’ 05] Relativistic Langevin Simulation: • stochastic implementation of HQ motion in expanding QGP-fireball • “hydrodynamic” evolution of bulk-matter b. T , v 2 Nuclear Modification Factor Elliptic Flow • resonances → large charm suppression+collectivity, not for bottom • v 2 “leveling off ” characteristic for transition thermal → kinetic

2. 3. 2 The first 5 fm/c for Quark-v 2 and -RAA Inclusive v 2 • RAA built up earlier than v 2

2. 3. 3 HQ Langevin Simulations: Hydro vs. Fireball Elastic p. QCD (charm) + Hydrodynamics a , g [Moore+Teaney ’ 04] s 1 , 3. 5 0. 5 , 2. 5 0. 25, 1. 8 • Tc=165 Me. V, t ≈ 9 fm/c • sg. Q ~ (as/m. D)2 as and m. D~g. T independent (m. D≡ 1. 5 T) • as=0. 4, m. D=2. 2 T ↔ D(2 p. T) ≈ 20 hydro ≈ fireball expansion [van Hees, Greco+RR ’ 05]

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 Fragmentation only • large suppression from resonances, elliptic flow underpredicted (? ) • bottom sets in at p. T~2. 5 Ge. V

2. 4. 2 Single-e± at RHIC: Resonances + Q-q Coalescence fq from p, K [Greco et al ’ 03] Nuclear Modification Factor Elliptic Flow • less suppression and more v 2 • anti-correlation RAA ↔ v 2 from coalescence (both up) • radiative E-loss at high p. T? !

2. 5 Model Comparisons to Recent PHENIX Data Single-e± Spectra [PHENIX ’ 06] • p. QCD radiative E-loss with 10 -fold upscaled transport coeff. • Langevin with elastic p. QCD + resonances + coalescence • Langevin with 2 -6 upscaled p. QCD elastic • coalescence essential for consistent RAA and v 2 • other mechanisms: 3 -body collisions, … [Liu+Ko’ 06, Adil+Vitev ‘ 06]

2. 5. 2 Transport Properties of (s)QGP Spatial Diffusion Coefficient ‹x 2›-‹x› 2=Dx·t, Dx=2 d·(T/m. Q)/g, Ds=Dx/2 d Charm-Quark Diffusion Viscosity-to-Entropy: Lattice QCD [Nakamura +Sakai ’ 04] • small spatial diffusion → strong coupling E. g. strongly coupled gauge theory (Ad. S/CFT): h/s=1/4 p, DHQ≈1/2 p. T resonances: DHQ≈4 -6/2 p. T , DHQ ~ h/s ≈ (1 -1. 5)/p

3. ) _ Potential Scattering in s. QGP Lattice Q-Q Free Energy Applications • → Schrödinger-Eq. → bound states (s. QGP) [Shuryak+ Zahed ’ 04, …] • scattering states + imaginary parts [Bielefeld Group ’ 04] → Lippmann-Schwinger Eq. [Mannarelli+RR ’ 05] Q-q- T-Matrix solve numerically

3. 2 Charm-Light Cross Sections with l. QCD-based Potential Temperature Evolution • interaction strength close to threshold 2 Channel Decomposition • meson and diquark channels dominant

3. 3 Friction Coefficients (Relaxation Rate): Lat-QCD vs. Resonance Model T ≈ 200 Me. V T ≈ 250 Me. V • uncertainty in potential extraction from lattice QCD • potential scattering comparable to resonance model close to Tc

3. 4 Charm-Quark Spectra at RHIC Nuclear Suppression Factor Elliptic Flow • supports importance of nonperturbative effects • radiative (2↔ 3) scattering?

4. ) Summary and Conclusions • Heavy quarks probe the (s)QGP: strong suppression, collectivity • Importance of elastic collisions • Indications for nonperturbative interactions • Supported by microscopic description: l. QCD-based T-matrix, scrutinize: l. QCD correlators, U 1 vs. F 1, finite-T quark masses • “Hadronic” correlations dominant (meson + diquark) ↔ natural connection to quark-coalescence at Tc [Ravagli+RR ’ 07] • Impact on other observables: light sector, quarkonia, dileptons, …

3. 2 Selfconsistent T-Matrix and Selfenergy [Mannarelli+RR ’ 05] - T-Matrices q-q T=1. 2 Tc T=1. 5 Tc T=1. 75 Tc Quark Self. Energy T=1. 5 Tc • assume mq(gluon)=0. 1 Ge. V • transition from bound (1. 2 Tc) to resonance states! • quark-width ≈0. 3 Ge. V≈(2/3 fm)-1 (≈ mass ↔ liquid!? ) • colored states, equat. of state?

5. 3. 2 Dileptons II: RHIC [R. Averbeck, PHENIX] [RR ’ 01] QG P • low mass: thermal! (mostly in-medium r) • connection to Chiral Restoration: a 1 (1260)→ pg , 3 p • int. mass: QGP (resonances? ) vs. cc- → e+e-X (softening? )