1 / 36

Heavy-Flavor Probes of Quark-Gluon Plasma and RHIC

This presentation discusses the use of heavy quarks (c and b) as probes of the Quark-Gluon Plasma (QGP) in heavy-ion collisions. It covers topics such as heavy quarkonia, heavy-quark diffusion, and quarkonium production in ultra-relativistic heavy-ion collisions. Theoretical and phenomenological constraints are discussed, along with the effects of the thermal medium on heavy quarks.

cbarrientes
Download Presentation

Heavy-Flavor Probes of Quark-Gluon Plasma and RHIC

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Heavy-Flavor Probes of Quark-Gluon Plasma and RHIC Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA CATHIE/TECHQM Workshop BNL (Upton, NY), 16.12.09

  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): • - quarkonia ↔ potential QCD • - heavy-quark diffusion ↔ elastic scattering, Fokker-Planck • → unified framework • Beyond perturbation theory (as expansion) • → resummations, bound + scattering states • Theoretical / phenomenological constraints essential • Heavy-ion collisions: • - initial-state effects (shadowing, absorption, formation time, …) • - medium effects: equilibrium properties, expansion collectivity

  3. Outline 1.) Introduction 2.) Heavy Quarkonia in QGP  Thermal Lattice QCD  Potential Models  “Corrections” 3.) Quarkonia in Heavy-Ion Collisions  Thermal Rate Equation  Suppression, Regeneration + “Tdiss” 4.) Heavy-Quark Diffusion in QGP  Fokker-Planck + T-Matrix  Heavy-Quark Observables at RHIC 5.) Conclusions

  4. 2.1 Quarkonium Correlators in Lattice QCD • direct computation of • Euclidean Correlation Fct. • accurate lattice “data” spectral function [Datta et al ‘04] hc J/y [Aarts et al ’07] • ~20% variation of S-wave charmonia ~ 0.9-3 Tc • Bound states survive? Spectral functions?! [Asakawa et al ’03, Iida et al ’06, Jakovac et al ‘07]

  5. 2.1.2 Heavy-Quark Free Energy in Lattice QCD • F1(r,T) = U1(r,T) – T S1(r,T) • V(r,T) ≡ X1(r,T) - X1(r=∞,T) • X1∞/2 ~ DmQ(T) (?) • examples: • (a) X1= F1 • => weak potential, eB(1.1Tc) ~ 50 MeV • DmQ(T)small • (b) X1=U1( U = ‹Hint› ) • => strong potential,eB(1.1Tc) ~ 500 MeV • DmQ(T)large • approximate compensation in • bound-state mass: Ey = 2mc0 + X1∞-eB [Kaczmarek+Zantow ’05]

  6. 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

  7. 2.2 Potential Models for Spectral Functions • well established in vacuum (EFT, lattice) • Schrödinger equation in medium • correlators: quark rescattering in continuum [Shuryak+Zahed ’04, Mocsy+Petreczky ‘06, Alberico et al ‘06, Wong ’07, Laine ’07, Ghiglieri et al ‘08…] • Lippmann-Schwinger equation [Mannarelli+RR ’05, Cabrera+RR ‘06] In-Medium Q-QT-Matrix: - - - Q-Q propagator: - bound + scattering states (threshold enhancements)

  8. 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

  9. q q 2.3 Quarkonium Widths in QGP → sensitive to binding energy (i.e., color screening) J/y Dissociation Rates NLO anti-/quarks NLO gluons as~0.25 as~0.5 [Grandchamp+RR ’01] [ Park et al ’07] • inelastic J/y width ~ (50-500) MeV

  10. 2.4 Further “Corrections” to Spectral Functions • 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 (usually 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 lQCD, extract Fa , Ua scalar •  implement into “extended T-Matrix approach” [Brown et al ‘05] [Philipsen ‘08] [Riek+RR in prep]

  11. 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

  12. Regeneration in QGP + HG: • - backward reaction (detailed balance!) if J/y survives → - ← J/y + g c + c + X [PBM et al ’01, Gorenstein et al ’02,Thews et al ’01, Grandchamp+RR ’01, Ko et al ’02, Cassing et al ’03, Zhu et al ’05, …] D - D J/y reaction rate equilibrium limit (y -width) - c c (links to spectral function) J/y 3.) Quarkonium Production in URHICs • 3-Stage Dissociation:nuclear (pre-eq) -QGP-HG • Stot = exp[-snucrL] exp[-GQGPtQGP ] exp[-GHGtHG ]

  13. 3.1.2 J/y Spectral Functions (schematic) Inelastic Width Spectral Function “Weak-Binding” Scenario “Strong-Binding” Scenario - • T>Tdiss : J/y → cc , • no formation • J/y mass =3.1GeV const • ↔ equilibrium limit

  14. 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, …]

  15. 3.1.4 Initial Condiations + Medium Evolution - • J/y (cc, y’), c-c production cross sections [p-p data, pQCD, …] • Cold Nuclear Matter effects: • - shadowing • - nuclear absorption • - pt broadening [p-A data, CGC, …] • (Thermal) fireball evolution: • - thermalization time (↔ initialT0), Tc • - expansion rate, lifetime, freezeout, … [hadron data, • hydrodynamics, transport,…] [Kharzeev et al ‘07, Ferreiro et al ‘08]

  16. 3.2 Charmonium at RHIC: Centrality Dependence • solve rate equation with thermal fireball,T0 = 310-340 MeV(MB-central) Strong-Binding Scenario Weak-Binding Scenario • weak-binding requires faster c-quark relaxation (tceq=9vs. 3 fm/c) • strong-binding favored? [Zhao+RR ‘09]

  17. 3.2.2 Comparison of Thermal Rate-Eqs. at RHIC RAA Nucl. Abs. 4 mb|0 mb Medium Evo. fireb. | hydro Width NLO+ | LO + direct |1/Q(T-Td) 2.5Tc|1.9Tc <pt 2> [Zhao+RR ‘09] [Liu,Qu,Xu+ Zhuang ‘09] • good agreement but different in detail • see also [Gunji et al ’07, Young et al ’09,…]

  18. 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 et al in prep] 4.) Heavy-Quark Diffusiion in the QGP • Brownian • Motion: Fokker Planck Eq. [Svetitsky ’88,…] Q thermalization rate diffusion coefficient

  19. 4.2 Charm-Quark T-Matrix + Thermalization Thermal Q-qT-Matrix Thermalization Rate • meson/diquark resonances for T <1.4Tc • thermalization rate ~ const

  20. 4.3 Thermalization Rate and Diffusion Coefficient g [1/fm] T [GeV] T [GeV] • “different” approaches related, e.g. AdS/CFT ↔ Coulomb • large coupling in pQCD calls for resummation • NB: suppression (RAA) early - elliptic flow (v2) “late”

  21. 4.4 Comparison of c-Quark RAA + v2 [26] [28] [115] [arXiv:0903.1096 hep-ph]

  22. 4.5 e± Spectra at RHIC T-mat T-mat T-mat T-mat [van Hees et al ‘07] • hadronic resonances at~Tc↔ quark coalescence • connects 2 “pillars” of RHIC: strong coupl. + coalescence

  23. 5.) Conclusions • Theoretical relations heavy quarks - quarkonia • - potential approaches (+ corrections) • - constraints from lattice QCD • (not yet conclusive: U1 ↔ Tcy~2Tc vs. F1 ↔ Tcy~1.3Tc) • - full heavy-quark(onium) many-body problem to be worked out • Quarkonium phenomenology • - “strong” J/y binding favored? (pt-data …) • - bottomonium suppression? • Open heavy flavor • - resonances close to Tc ? (strong coupling + coalescence…) • - RHIC non-photonic e± Ds (2pT) ≈ 5 , v2-RAA correlation • - scrutinize medium evolution, Fokker-Planck, d-Au …

  24. 3.2.3 Rapidity Dependence at RHIC Thermal Rate-Eq Approach • regeneration yield sensitive to dNc/dy • regeneration yield alone problematic • with pt-dependence • additional shadowing at forward y [Kharzeev et al. ‘07, Ferreiro et al. ‘08] [Zhao+RR ‘09]

  25. 1.2 J/y Suppression in Heavy-Ion Collisions • Universal suppression pattern at SPS and RHIC • as function produced-particle number?

  26. _ 2.3.2 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]

  27. 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]

  28. 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]

  29. Satz, Digal, Fortunato Rapp, Grandchamp, Brown Capella, Ferreiro • Percolation • Plasma • Comovers NA60 preliminary 3.5 Charmonium Observables at SPS Pb(158AGeV)-PbIn(158AGeV) –In • QGP-suppression prevalent • “jumps” / ”plateaus” in centrality? [Grandchamp etal ’03]

  30. 2.2 Color Magnetic Interaction and Constraints • Color-Magnetic “Breit” Interaction • VQ1Q2(r) → VQ1Q2(r) ( 1 – v1· v2 ) [G.E. Brown ’52, Brown et al ‘04] - Vacuum “Spectroscopy” Perturbative Q-q Scattering mc0 =1.4 GeV - [van Hees et al ‘09] [Riek et al ‘09] - • Born approx. TQq = VQq • recovers pQCD within ~20% • Q-Q and Q-q states ~ o.k. • spin-interactionsO(1/mQ)

  31. 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]

  32. 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)

  33. 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), …

  34. 2.2.1 Color Screening + Quarkonium Binding in QGP e.g. screened Cornell pot.: Charmonium Bottomonium ~Tc ~Tc m~ gT [GeV] [Matsui+Satz ’86, Karsch,Mehr+Satz ’88, Wong ’04, …] m~ gT [GeV] • quarkonium binding substantially reduced aboveTc

  35. 2.3.2 Bottomonium Reaction Rates in QGP • color-screening accelerates dissociation • significance at RHIC: tY ≈ 50 →5 fm/c [Grandchamp et al. ’05]

  36. 3.3.3 Dissociation Temperature Suppression only (Hydro) Including Regeneration Tdiss= 2.0 Tc 1.2 Tc “threshold melting” “finite width” [Zhao+RR ‘08] • finite width and regeneration • wash out “step” structure [Gunji et al. ‘07]

More Related