Heavy Quarkonium in Hot Nuclear Matter Ralf Rapp

Heavy Quark/onium in Hot Nuclear Matter Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA INT Program (Week 7) on “Quantifying the Properties of Hot QCD Matter” INT (Seattle), 06. -09. 07. 10

1. ) Introduction: Virtues of Heavy Quarks (c, b) • “Large” scale m. Q >> LQCD , T - factorization in production; thermal medium: pth 2 ~ 2 m. Q T >> T 2 • Interactions spacelike (“low” pt): - quarkonium: potential QCD - heavy-quark diffusion: Brownian motion Q Q → unified framework • Beyond perturbation theory (as expansion) → resummations, bound + scattering states • Constraints essential (lat. QCD, p. QCD, vacuum spectrum, …) • Heavy-ion collisions: - “initial-state” effects - medium effects: equilibrium properties, expansion collectivity

1. 2 Charm/onium Suppression at SPS + RHIC Anomalous J/y Suppression Heavy-Quark Suppression+Flow • Same force operative for quarkonium (un)binding + heavy-quark transport?

1. ) Introduction Outline 2. ) T-Matrix for Heavy Quark/onium in QGP Vacuum Spectroscopy, In-Medium Potentials Spectral + Correlation Functions 3. ) Quarkonia in Heavy-Ion Collisions Thermal Rate Equation Suppression vs. Regeneration 4. ) Heavy-Quark Diffusion in QGP Fokker-Planck + Thermalization Observables at RHIC 5. ) Conclusions

2. ) Heavy-Quark Potential + Thermal T-Matrix • HQ potential well established in vacuum (EFT, lattice, spectroscopy) • Quark-Gluon Plasma: bound+scattering states (quarkonia + HQ transport) • Lippmann-Schwinger equation [Mannarelli+RR ’ 05, Cabrera+RR ’ 06, Riek+RR ‘ 09] In-Medium Q-Q T-Matrix: - Q-Q propagator: - importance of threshold effects • 2 -body potential VL at finite temperature?

2. 2 Heavy-Quark Free Energy in Lattice QCD F 1(r, T) = U 1(r, T) – T S 1(r, T) • Potential “Choices” : (a) Free energy F 1 => weak potential, e. B(1. 1 Tc) ~ 50 Me. V Dm. Q(T) ~ F 1(r=∞, T) small (b) Internal Energy U 1 ( U = ‹Hint› ) => strong potential, e. B(1. 1 Tc) ~ 500 Me. V Dm. Q(T) ~ U 1(r=∞, T) large • approximate compensation in bound-state mass: Ey = 2 mc 0 + 2 Dm. Q - e. B • need improved ways to extract HQ potential [Kaczmarek+Zantow ’ 05]

2. 3 Corrections to Heavy-Quark Potential • Relativistic effects - kinematics - magnetic interaction → “Breit” correction: [Brown et al ‘ 52, ‘ 05] VQ 1 Q 2(r) → VQ 1 Q 2(r) ( 1 – v 1 · v 2 ) (↔ Poincaré-invariance, p. QCD) • Retardation effects - 4 -D → 3 -D reduction of Bethe-Salpeter equation - energy transfer fixed (q 0=0), off-shell behavior ambiguous • Gauge dependence of color-singlet free energy [Philipsen ‘ 08] • Field-theoretic ansatz: [Megias et al ‘ 07] color-Coulomb: vector , string: - fit color-average free energy to lat. QCD implement into “extended T-Matrix approach” scalar [Riek+RR ‘ 10]

2. 3. 2 Temperature Dependence of Fit Parameters In-Medium HQ Free Energies Model Parameters • as ~ 0. 3 • screening of color-Coulomb + string term • “Debye masses” ~ T

2. 4. 1 Constraints I: Vacuum Spectroscopy Quarkonia D-Mesons • no hyperfine splitting • (bare) masses adjusted to ground state • ~ ± 50 Me. V accuracy

2. 4. 2 Constraints II: High-Energy Q-q Scattering Born Approximation compared to Perturbative QCD • Breit correction essential

2. 5 Quarkonium Spectral Functions in Medium 2. 5. 1 Lattice-QCD Correlators • direct computation of Euclidean Correlation Fct. spectral function [Datta et al ‘ 04] hc J/y [Asakawa et al ’ 03, Iida et al ’ 06, Aarts et al ‘ 07, Jakovac et al ‘ 07] • ~20% variation for S-wave charmonia ~ 0. 9 -3 Tc • Bound states survive above Tc? !

2. 5. 2 T-Matrix Spectral Functions with Potential U Euclidean Correlator Ratio S-Wave Spectral Function (narrow-width limit) • S-wave ground state “melts” at Tdiss ≈ 2 Tc • correlator ratios within 30% (3 D reduction scheme)

2. 5. 3 T-Matrix Spectral Functions with Potential F S-Wave Spectral Function Euclidean Correlator Ratio • S-wave ground state “melts” at Tdiss ≈ 1. 3 Tc • reduced c-c- threshold → low-energy strength [Cabrera+RR ’ 06, Riek+RR ‘ 09]

2. 5. 4 Importance of Confining Force J/y Υ

2. 6 Charmonium Widths in QGP q q → sensitive to binding energy (i. e. , color screening) J/y Dissociation Rates S-Wave Spectral Function J/y as~0. 25 • J/y lifetime ~ 1 -4 fm/c [Grandchamp+RR ’ 01] Gymed=200 Me. V • accelerates “melting”: Tdiss ≈ 1. 6 Tc • correlator ratio temperature-stable

2. 6. 2 Momentum Dependence of Inelastic Width • dashed lines: gluo-dissociation • solid lines: quasifree dissociation q q _ • similar to full NLO calculation [Zhao+RR ‘ 07] [Park et al ‘ 07]

2. 6. 3 Relation of Quarkonium Widths to EFT • Singlet-octet transition • Landau damping q q

3. ) Quarkonium Production in URHICs • Regeneration in QGP + HG: - detailed balance reaction rate (y -width) [PBM et al ’ 01, Gorenstein et al ’ 02, Thews et al ’ 01, Grandchamp+RR ’ 01, Ko et al ’ 02, Cassing et al ’ 03, Zhuang et al ’ 05, …] → c + c- + X J/y + g ← equilibrium limit D D J/y c- c J/y • Input from Thermodynamic T-Matrix (weak/strong binding) Gy mc * e By

3. 1 Inputs and Parameters • Input - J/y (cc, y’), c-c- production cross sections [p-p data [PHENIX] ] - “Cold Nuclear Matter”: shadowing, nuclear absorption, pt broadening [p-A data] - Thermal fireball evolution: thermalization time (↔ initial T 0), expansion rate, lifetime, Tc , freezeout … [hadron data, hydrodynamics] • Parameters - strong coupling as controls Gdiss - schematic relaxation for c-quark equilibration: Nyeq (t)~ Nytherm(t) · [1 -exp(-t/tceq)] _

3. 2 Centrality Dependence of J/y at SPS + RHIC Strong-Binding Scenario (U) Weak-Binding Scenario (F) [Zhao+RR in prep] • regeneration controlled by c-quark relaxation time (tceq = 6 vs. 3 fm/c) • similar total yield, but different composition

3. 3 p. T-Dependence of J/y at SPS + RHIC Strong Binding (U) Weak Binding (F) • weak binding problematic with pt-dependence? !

3. 3. 2 p. T-Dependence II: Blast Wave at RHIC Regeneration only (Stat. Model) Rate-Equation (strong bind. ) Au-Au 200 AGe. V [Andronic et al. ‘ 07] • blast wave at ~Tc too soft? • lever arm for direct prod. at high p. T?

3. 3. 3 Charm-Quark p. T-Spectra and Regeneration • microscopic calculation of gain term c + c- + g → J/y + g • supports sensitivity to thermal relaxation time of c quarks

4. ) Heavy-Quark Diffusion in the QGP Q • Brownian Motion: Fokker Planck Eq. [Svetitsky ’ 88, …] thermalization rate • p. QCD elastic scattering: g -1 = ttherm ≥ 20 fm/c slow q, g c diffusion coefficient [Svetitsky ’ 88, Mustafa et al ’ 98, Molnar et al ’ 04, Zhang et al ’ 04, Hees+RR ’ 04, Teaney+Moore ’ 04, Peshier, Gossiaux+Aichelin ‘ 09] • In-medium heavy-light T-matrix: direct connection to quarkonia! [van Hees et al ’ 07, Riek+RR ‘ 10]

4. 2 Charm-Quark T-Matrix + Thermalization Thermal Q-q T-Matrix g [1/fm] Thermalization Rate T [Ge. V] • meson/diquark resonances for T < 1. 5 Tc • factor 3 -4 (~2) larger than pert. QCD for U (F) potential [Riek+RR ‘ 10]

4. 3 e± Spectra at RHIC T-mat [van Hees et al ‘ 07] • hadronic resonances at ~Tc ↔ quark coalescence • connects 2 “pillars” of RHIC: strong coupl. + coalescence

5. ) Conclusions • Thermodynamic T-matrix for heavy quarks + quarkonia - vacuum: spectroscopy + p. QCD limit - in-medium potential from lattice QCD? U 1 (Tdy~2 Tc) , F 1 (Tdy~1. 3 Tc) , or else … - confining force mandatory for realistic calculations • Quarkonium phenomenology - “strong” vs. “weak” J/y binding (pt-data, lever arm, …) - bottomonium suppression? (less regeneration …) • Open heavy flavor - resonances close to Tc ? (strong coupling + coalescence …) - RHIC non-photonic e± Ds (2 p. T) ≈ 5 - scrutinize medium evolution, Fokker-Planck, d-Au …

3. 2. 3 Rapidity Dependence at RHIC Thermal Rate-Eq Approach • regeneration yield sensitive to d. Nc/dy • hot matter effects insufficient • additional shadowing at forward y (assuming constant sabs) [Kharzeev et al. ‘ 07, Ferreiro et al. ‘ 08] [Zhao+RR in prep]

3. 2. 5 Momentum Spectra Au-Au 200 AGe. V • regeneration part → blast-wave at Tc • regeneration at low p. T • high p. T: formation time ( bottom feeddown, … [Zhao+RR ’ 07, ‘ 08] ), [Karsch+Petronzio ’ 87, Blaizot+Ollitrault ‘ 87]

3. 2. 4 Momentum Spectra and Elliptic Flow • regeneration at low pt → small v 2 • direct component at high pt → small v 2 [Zhao+RR ’ 08, Zhuang et al ‘ 06]

2. 4. 2 Example from “Extended T-Matrix Model” S-Wave Spectral Function hc • cc- propagator with Gc= 100 Me. V: • S-wave “melting” Tdiss ≈ 1. 5 -2 Tc • correlator ratio temperature-stable Euclidean Correlator Ratio

g [1/fm] 4. 3 Thermalization Rate and Diffusion Coefficient T [Ge. V] • Factor ~3 -4 larger thermalization rates than in pert. QCD • “different” approaches related, e. g. Ad. S/CFT ↔ Coulomb

2. 4 Mesonic Spectral Functions + Correlators • Euclidean Correlation Function (precise lat-QCD data avail. !) Correlator Ratio:

2. 2. 2 Potential Models in the QGP ~F 1 potential [Mocsy+ Petreczky ’ 05, ‘ 08] U 1 potential [Cabrera +RR ‘ 06] hc mcc=1. 7 Ge. V mc * • F 1 low threshold (2 mc~ 2. 7 Ge. V), ground state Tdiss ~ 1. 2 Tc • U 1 decreasing threshold and e. B, Tdiss ~2. 5 Tc both scenarios compatible with lat-QCD

3. 1. 3 Equilibrium Limit (Statistical Model) • fixed c-c- number: • equilibrium Y number: • (very) sensitive to open-charm spectrum [Grandchamp et al ’ 03, Andronic et al ’ 07, …] • thermal relaxation for c-quark spectra:

2. 1. 3 In-Medium Charm-Quark Mass in LQCD [Kaczmarek +Zantow ’ 05] [Velytsky et al ’ 09] F • U : large variation close to Tc – mass interpretation? ! • fit quark-number fluctuations with zero-width quasiparticle model c(T) ~ ∂2 P / ∂2 mc

3. 3. 4 Rapidity Dependence at RHIC Statistical Model • reproduced in statistical hadronization model (GC ensemble) [Andronic et al. ’ 07] • more problematic in dynamic approaches [Capella et al. ’ 07, Zhao+RR ‘ 08] • additional shadowing at forward y? [Kharzeev et al. ‘ 07, Ferreiro et al. ‘ 08] Thermal Rate-Eq Approach

3. 4 Upsilon at RHIC No Color-Debye Screening With Color-Debye Screening [Grandchamp et al. ’ 05] • (1 S, 2 S) suppression unambiguous QGP signature ? ! • NB: 50% feed-down on (1 S)

3. 3 Heavy-Quark Spectra at RHIC • relativistic Langevin simulation in elliptic expanding fireball background Nuclear Modification Factor Elliptic Flow p. T [Ge. V] • T-matrix approach ≈ effective resonance model • similar to “coll. dissoc. ” [Adil+Vitev ’ 07]; radiative E-loss? (2↔ 3), …

2. 3. 2 Bottomonium Reaction Rates in QGP • color-screening accelerates dissociation • significance at RHIC: t. Y ≈ 50 → 5 fm/c [Grandchamp et al. ’ 05]