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Heavy Quark/onium in Hot Nuclear Matter

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.

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Heavy Quark/onium in Hot Nuclear Matter

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  1. Heavy Quark/oniumin 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

  2. 1.) Introduction: Virtues of Heavy Quarks(c,b) • “Large” scale mQ >> LQCD , T • - factorization in production; thermal medium: pth2 ~ 2mQ T >> T2 • Interactions spacelike (“low” pt): • - quarkonium: potential QCD • - heavy-quark diffusion: Brownian motion • → unified framework • Beyond perturbation theory (as expansion) • → resummations, bound + scattering states • Constraints essential (latQCD, pQCD, vacuum spectrum,…) • Heavy-ion collisions: • - “initial-state” effects • - medium effects: equilibrium properties, expansion collectivity Q Q

  3. 1.2 Charm/onium Suppression at SPS + RHIC Heavy-Quark Suppression+Flow Anomalous J/y Suppression • Same force operative for • quarkonium (un)binding + heavy-quark transport?

  4. Outline 1.) Introduction 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

  5. 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-QT-Matrix: - - • -Q-Q propagator: • importance of threshold effects • 2-body potential VL at finite temperature?

  6. 2.2 Heavy-Quark Free Energy in Lattice QCD • F1(r,T) = U1(r,T) – T S1(r,T) • Potential “Choices” : • (a) Free energy F1 • => weak potential, eB(1.1Tc) ~ 50 MeV • DmQ(T)~ F1(r=∞,T) small • (b) Internal Energy U1( U = ‹Hint› ) • => strong potential,eB(1.1Tc) ~ 500 MeV • DmQ(T) ~ U1(r=∞,T) large • approximate compensation in • bound-state mass: Ey = 2mc0 + 2DmQ-eB • need improved ways to extract HQ potential [Kaczmarek+Zantow ’05]

  7. 2.3 Corrections to Heavy-Quark Potential • Relativistic effects • - kinematics • - magnetic interaction → “Breit” correction: • VQ1Q2(r) → VQ1Q2(r) ( 1 – v1 · v2 )(↔ Poincaré-invariance, pQCD) • Retardation effects • - 4-D → 3-D reduction of Bethe-Salpeter equation • - energy transfer fixed (q0=0), off-shell behavior ambiguous • Gauge dependence of color-singlet free energy • Field-theoretic ansatz: • [Megias et al ‘07] • color-Coulomb: vector , string: • - fit color-average free energy to lat. QCD scalar •  implement into “extended T-Matrix approach” [Brown et al ‘52, ‘05] [Philipsen ‘08] [Riek+RR ‘10]

  8. 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

  9. 2.4.1 Constraints I: Vacuum Spectroscopy Quarkonia D-Mesons • no hyperfine splitting • (bare) masses adjusted to ground state • ~ ±50 MeV accuracy

  10. 2.4.2 Constraints II: High-Energy Q-q Scattering Born Approximation compared to Perturbative QCD • Breit correction essential

  11. 2.5 Quarkonium Spectral Functions in Medium2.5.1 Lattice-QCD Correlators • direct computation of • Euclidean Correlation Fct. spectral function [Datta et al ‘04] hc [Asakawa et al ’03, Iida et al ’06, Aarts et al ‘07, Jakovac et al ‘07] J/y • ~20%variation for S-wave charmonia ~ 0.9-3 Tc • Bound states survive above Tc?!

  12. 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% (3D reduction scheme)

  13. 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]

  14. 2.5.4 Importance of Confining Force J/y Υ

  15. q q 2.6 Charmonium Widths in QGP → sensitive to binding energy (i.e., color screening) S-Wave Spectral Function J/y Dissociation Rates J/y as~0.25 Gymed=200MeV • accelerates “melting”: Tdiss ≈ 1.6 Tc • correlator ratio temperature-stable • J/y lifetime ~ 1-4 fm/c [Grandchamp+RR ’01]

  16. q q _ 2.6.2 Momentum Dependence of Inelastic Width • dashed lines: gluo-dissociation • solid lines: quasifree dissociation • similar to full NLO calculation [Park et al ‘07] [Zhao+RR ‘07]

  17. q q 2.6.3 Relation of Quarkonium Widths to EFT • Singlet-octet • transition • Landau • damping

  18. D - D J/y reaction rate equilibrium limit (y -width) - c c J/y 3.) Quarkonium Production in URHICs [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, …] • Regeneration in QGP + HG: • -detailed balance → - ← J/y + g c + c + X • Input from Thermodynamic T-Matrix (weak/strong binding) Gy eBy mc*

  19. _ 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 (↔ initialT0), • expansion rate, lifetime, Tc , freezeout … • [hadron data, hydrodynamics] - • Parameters • - strong coupling ascontrols Gdiss • - schematic relaxation for c-quark equilibration: • Nyeq (t)~ Nytherm(t) · [1-exp(-t/tceq)]

  20. 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=6vs. 3 fm/c) • similar total yield, but different composition

  21. 3.3 pT-Dependence of J/y at SPS + RHIC Strong Binding (U) Weak Binding (F) • weak binding problematic with pt-dependence?!

  22. 3.3.2 pT-Dependence II: Blast Wave at RHIC Regeneration only (Stat. Model) Rate-Equation (strong bind.) Au-Au 200AGeV [Andronic et al. ‘07] • blast wave at ~Tc too soft? • lever arm for direct prod. at high pT?

  23. 3.3.3 Charm-Quark pT-Spectra and Regeneration - • microscopic calculation of gain term c + c + g → J/y + g • supports sensitivity to thermal relaxation time of c quarks

  24. pQCD elastic scattering:g-1= ttherm ≥ 20 fm/cslow q,g c [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.) Heavy-Quark Diffusion in the QGP • Brownian • Motion: Fokker Planck Eq. [Svetitsky ’88,…] Q thermalization rate diffusion coefficient

  25. 4.2 Charm-Quark T-Matrix + Thermalization Thermal Q-qT-Matrix Thermalization Rate g [1/fm] T [GeV] • meson/diquark resonances for T <1.5Tc • factor 3-4 (~2) larger than pert. QCD • for U (F) potential [Riek+RR ‘10]

  26. 4.3 e± Spectra at RHIC T-mat T-mat [van Hees et al ‘07] • hadronic resonances at~Tc↔ quark coalescence • connects 2 “pillars” of RHIC: strong coupl. + coalescence

  27. 5.) Conclusions • Thermodynamic T-matrix for heavy quarks + quarkonia • - vacuum: spectroscopy + pQCD limit • - in-medium potential from lattice QCD? • U1 (Tdy~2Tc) , F1 (Tdy~1.3Tc) , 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 (2pT) ≈ 5 • - scrutinize medium evolution, Fokker-Planck, d-Au …

  28. 3.2.3 Rapidity Dependence at RHIC Thermal Rate-Eq Approach • regeneration yield sensitive to dNc/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]

  29. high pT: formation time ( ), • bottom feeddown, … [Karsch+Petronzio ’87, Blaizot+Ollitrault ‘87] 3.2.5 Momentum Spectra Au-Au 200AGeV • regeneration part → blast-wave at Tc • regeneration at low pT [Zhao+RR ’07, ‘08]

  30. 3.2.4 Momentum Spectra and Elliptic Flow • regeneration at low pt → small v2 • direct component at high pt → small v2 [Zhao+RR ’08, Zhuang et al ‘06]

  31. 2.4.2 Example from “Extended T-Matrix Model” S-Wave Spectral Function Euclidean Correlator Ratio hc - • ccpropagator with Gc= 100 MeV: • S-wave “melting” Tdiss ≈ 1.5-2 Tc • correlator ratio temperature-stable

  32. 4.3 Thermalization Rate and Diffusion Coefficient g [1/fm] T [GeV] T [GeV] • Factor ~3-4 larger thermalization rates than in pert. QCD • “different” approaches related, e.g. AdS/CFT ↔ Coulomb

  33. 2.4 Mesonic Spectral Functions + Correlators • Euclidean Correlation Function (precise lat-QCD data avail.!) Correlator Ratio:

  34. mc=1.7GeV mc* 2.2.2 Potential Models in the QGP [Mocsy+ Petreczky ’05,‘08] [Cabrera +RR ‘06] ~F1potential U1potential hc mc=1.7GeV • F1 low threshold (2mc~ 2.7GeV), • ground state Tdiss ~ 1.2 Tc • U1 decreasing threshold and eB, • Tdiss ~2.5Tc •  both scenarios compatible with lat-QCD

  35. 3.1.3 Equilibrium Limit (Statistical Model) - • fixed c-c number: • equilibrium • Y number: • (very) sensitive to • open-charm spectrum • thermal relaxation for • c-quark spectra: [Grandchamp et al ’03, Andronic et al ’07, …]

  36. 2.1.3 In-Medium Charm-Quark Mass in LQCD [Kaczmarek +Zantow ’05] [Velytsky et al ’09] F • U: large variation close toTc • – mass interpretation?! • fit quark-number fluctuations with • zero-width quasiparticle model • c(T) ~ ∂2P / ∂2mc

  37. 3.3.4 Rapidity Dependence at RHIC Statistical Model Thermal Rate-Eq Approach • reproduced in statistical hadronization • model (GC ensemble) [Andronic et al. ’07] • more problematic in dynamic • approaches • additional shadowing at forward y? [Capella et al. ’07, Zhao+RR ‘08] [Kharzeev et al. ‘07, Ferreiro et al. ‘08]

  38. 3.4 Upsilon at RHIC No Color-Debye Screening With Color-Debye Screening [Grandchamp et al. ’05] • (1S,2S) suppression unambiguous QGP signature ?! • NB: 50% feed-down on(1S)

  39. 3.3 Heavy-Quark Spectra at RHIC • relativistic Langevin simulation in elliptic expanding fireball background Nuclear Modification Factor Elliptic Flow pT [GeV] pT [GeV] • T-matrix approach ≈ effective resonance model • similar to “coll. dissoc.” [Adil+Vitev ’07]; radiative E-loss? (2↔3), …

  40. 2.3.2 Bottomonium Reaction Rates in QGP • color-screening accelerates dissociation • significance at RHIC: tY ≈ 50 →5 fm/c [Grandchamp et al. ’05]

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