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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), 07.10.08 Theory and Phenomenology of Heavy Flavor at RHIC
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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?
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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
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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]
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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]
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2.2.2 Charm-Light QuarkT-Matrix + Drag Coefficient supports effective resonance model: S-wave mesons and diquarks up to 1.2-1.5 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
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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=180-250 MeV Lat-QCD T QCD ~ 250 MeV
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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?
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2.5 Comparison of Drag Coefficients pert. QCD with running coupling ~ AdS/CFT increase with temperature except T-matrix (melting resonances)
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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]
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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
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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
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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
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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]
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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
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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
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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) ≈ 4-6 - v 2 - R AA correlation revealing (coalescence? k t -broad.? ) - scrutinize medium evolution, Fokker-Planck, … - D/B separation, correlations, quarkonia, …
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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]
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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
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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
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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
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3.2.4 Temperature Dependence of Charm-Quark Mass significant deviation only close to T c
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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
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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
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less suppression and more v 2 anti-correlation R AA ↔ v 2 from coalescence (both up) radiative E-loss at high p T ?! 2.4.2 Single-e ± at RHIC: Resonances + Q-q Coalescence f q from , K Nuclear Modification Factor Elliptic Flow [Greco et al ’03]
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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
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