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This paper discusses the role of heavy quarks, particularly c and b quarks, in the Quark-Gluon Plasma produced at RHIC and LHC accelerators. It covers their sensitivity to thermalization, energy loss, and coalescence, as well as their relation to observables like dileptons and quarkonia. The relevant interactions of heavy quarks at low and intermediate momenta are explored through various approaches, including lattice QCD-based potentials and T-Matrix calculations. The study also examines observables at RHIC such as centrality and pT spectra, providing insights into heavy quark dynamics in the QGP.
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Heavy Quarks in sQGPand Observables at RHIC + LHC Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees, D. Cabrera, X. Zhao, V. Greco, M. Mannarelli Heavy Quark Workshop Berkeley National Laboratory, 02.11.07
transport in QGP, hadronization 1.) Introduction: Heavy Quarks at RHIC • c, b quarks (more!?) sensitive to: • - thermalization (low pT) • - energy loss (high pT) • - coalescence (int. pT?) • Direct relation to other observables • intermediate-mass dileptons: • → e+e- X competes with thermal (QGP) radiation • quarkonia: • - interaction of c, b within bound state • - regeneration → Y What are the relevant interactions of heavy quarks at low/intermediate pT?
Outline 1.) Introduction HQ Observables in URHICs 2.) Heavy Quarkonia in QGP Charmonium Spectral + Correlation Functions Lattice-QCD based Potential Approach (T-Matrix!) Suppression vs. Regeneration at RHIC 3.) Open Heavy Flavor in QGP Heavy-Light Quark T-Matrix HQ Selfenergies + Transport Coefficients HQ and e± Spectra 4.)Conclusions
accurate lattice “data” forEuclidean Correlator hc cc [Datta et al ‘04] • S-wave charmonia little changed to ~2Tc • similar in other lQCD studies[Iida et al ’06, Jakovac et al ’07, Aarts et al ’07] 2.1 Quarkonia in Lattice QCD • direct computation of • Euclidean Correlation Fct. spectral function
- Q-QT-Matrix: 2.2 Potential-Model Approaches for Spectral Fcts. s/w2 • Schrödinger Eq. for bound • state + free continuum • sy(w) = Fy2d(w - my )+w2Q(w-Ethr) fythr • - improved for rescattering J/y [Shuryak et al ’04, Wong ’05, Alberico et al ’06, Mocsy+Petreczky ’06] Y’ cont. w Ethr • Lippmann-Schwinger-Eq. • for [Mannarelli+RR ’05,Cabrera+RR ‘06] - 2-quasi-particle propagator: - bound+scatt. states, nonperturbative threshold effects (large!) • Correlator: L=S,P
2.2.2 Uncertainty I: “Lattice QCD-based” Potentials • accurate lattice “data” forfree energy:F1(r,T) = U1(r,T) – T S1(r,T) • (much) smaller binding for • V1=F1, V1 = (1-a) U1 + a F1 [Cabrera+RR ’06; Petreczky+Petrov’04] [Wong ’05; Kaczmarek et al ‘03]
2.3 Charmonium Spectral Functions in QGP withinT-Matrix Approach (lattice U1 Potential) Fixedmc=1.7GeV In-mediummc* (U1subtraction) hc hc • gradual decrease of binding, rescattering enhancement! • hc , J/y survive until ~2.5Tc , ccup to ~1.2Tc
2.4.1 Charmonium Correlators I: S-Waves • lattice U1-potential, in-medium mc* [Cabrera+RR in prep] T-Matrix Approach [Aarts et al. ‘07] Lattice QCD J/y hc • fair agreement!
2.4.2 Charmonium Correlators II: P-Waves • lattice U1-potential, in-medium mc* [Cabrera +RR in prep] T-Matrix Approach [Aarts et al. ‘07] Lattice QCD cc0 cc1 • fair agreement!
2.5 Observables at RHIC: Centrality + pT Spectra • update of ’03 predictions: - 3-momentum dependence • - less nucl. absorption + c-quark thermalization [X.Zhao+RR in prep] • direct ≈ regenerated (cf. ) • sensitive to: tctherm , mc* , Ncc [Yan et al. ‘06]
_ _ q q Microscopic Calculations of Diffusion: q,g c • pQCD elastic scattering:g-1= ttherm ≥20 fm/cslow [Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04] • D-/B-resonance model:g-1= ttherm ~ 5 fm/c “D” parameters: mD , GD c c • new development: lQCD-potential scattering (no parameter) [van Hees et al. ’07] 3.) Heavy Quarks in the QGP • Brownian • Motion: Fokker Planck Eq. [Svetitsky ’88,…] Q scattering rate diffusion constant
coalescence essential for • consistent RAA and v2 • other mechanisms: • 3-body collisions, … [Liu+Ko’06, Adil+Vitev ‘06] 3.2 Model Comparisons to Recent PHENIX Data Single-e±Spectra [PHENIX ’06] • pQCD radiative E-loss with • 10-fold upscaled transport coeff. • Langevin with elastic pQCD + • resonances + coalescence • Langevin with 2-6 upscaled • pQCD elastic
3.2.2 Transport Properties of (s)QGP ‹x2›-‹x›2 ~ Ds·t , Ds ~ 1/g Spatial Diffusion Coefficient: Charm-Quark Diffusion Viscosity-to-Entropy: Lattice QCD [Nakamura +Sakai ’04] • small spatial diffusion → strong coupling • E.g. AdS/CFT correspondence:h/s=1/4p, DHQ≈1/2pT • resonances: DHQ≈4-6/2pT , DHQ ~ h/s ≈ (1-1.5)/p
3.3 Potential Scattering in sQGP Q-qT-Matrix • T-matrix for Q-q scatt. in QGP • solve numerically given VQq (p,p’) • Casimir scaling for color channels a [Mannarelli+RR ’05] • determination of potential • -fit latticeQ-Qfree energy • - Fourier transfo. + • partial-wave exp. • - relativist. correc. • for finite mQ,q • still significant • uncertainty _ [Shuryak+ Zahed ’04] [Wong ’05]
3.3.2 Charm-Light T-Matrix with lQCD-based Potential Temperature Evolution + Channel Decomposition [van Hees, Mannarelli, Greco+RR ’07] • meson and diquarkS-wave resonances up to 1.2-1.5Tc • P-waves and (repulsive) color-6, -8 channels suppressed
3.3.3 Charm-Quark Selfenergy + Transport Selfenergy Friction Coefficient • charm quark widths Gc = -2 ImSc~ 200MeV close to Tc • friction coefficients decrease(!) with increasing T !
3.4 Maximal “Interaction Strength” in the sQGP • potential-based description ↔ strongest interactions close to Tc • consistent with minimum in h/s at ~Tc • cf. bottom-up (hadron gas) + top-down (pQCD) extrapolations • strong hadronic correlations at Tc • ↔ quark coalescence! [Kapusta ’06]
3.5.1 Charm-Quark Spectra at RHIC • relativistic Langevin simulation in thermal fireball background Elliptic Flow Nuclear Suppression Factor • importance of nonperturbative effects supported • radiative (2↔3) scattering?
3.6 Heavy-Quark + Single-e± Spectra at LHC • relativistic Langevin simulation in thermal fireball background • resonances inoperative at T>2Tc , coalescence at Tc • harder input spectra, slightly more suppression RAA similar to RHIC
4.) Summary and Conclusions • T-matrix approach with lQCD internal energy (UQQ): • S-wave charmonia survive up to ~2.5Tc, • supported by lQCD correlators + spectral functions • T-matrix approach for heavy-light scattering: • large c-quark width + small diffusion (elastic, nonperturbative) • “Hadronic” correlations dominant (meson + diquark) • - maximum strength close to Tc ↔ minimum in h/s !? • - naturally merge into quark coalescence at Tc[Ravagli+RR ’07] • Observables: quarkonia, HQ suppression+flow, dileptons,… • Consequences for light-quark sector? Potential approach?
3.5.2 The first 5 fm/c for Charm-Quark v2 + RAA Inclusive v2 • RAA built up earlier than v2
2.3.3 HQ Langevin Simulations: Hydro vs. Fireball Elastic pQCD (charm) + Hydrodynamics [Moore+Teaney ’04] as , g 1 , 3.5 0.5 , 2.5 0.25,1.8 • Tc=165MeV, • t ≈ 9fm/c • sgQ ~ (as/mD)2 • as and mD~gT • independent • (mD≡1.5T) • as=0.4, mD=2.2T • ↔ D(2pT) ≈ 20 • hydro ≈ • fireball • expansion [van Hees,Greco+RR ’05]
Fragmentation only • large suppression from resonances, elliptic flow underpredicted (?) • bottom sets in at pT~2.5GeV 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
2.4.2 Single-e± at RHIC: Resonances + Q-q Coalescence fqfrom p, K [Greco et al ’03] Elliptic Flow Nuclear Modification Factor • less suppression and morev2 • anti-correlation RAA ↔ v2 from coalescence (both up) • radiative E-loss at high pT?!
Nuclear Modification Factor Elliptic Flow • resonances → large charm suppression+collectivity, not for bottom • v2 “leveling off ” characteristic for transition thermal → kinetic 2.3 Heavy-Quark Spectra at RHIC • Relativistic Langevin Simulation: • stochastic implementation of HQ motion in expanding QGP-fireball • “hydrodynamic” evolution of bulk-matterbT , v2 [van Hees,Greco+RR ’05]
2.1.3 Thermal Relaxation of Heavy Quarks in QGP Charm: pQCD vs. Resonances Charm vs. Bottom pQCD “D” • tctherm ≈ tQGP ≈ 3-5 fm/c • bottom does not thermalize • factor ~3 faster with • resonance interactions!
5.3.2 Dileptons II: RHIC [R. Averbeck, PHENIX] [RR ’01] QGP • low mass: thermal! (mostly in-medium r) • connection to Chiral Restoration: a1 (1260)→ pg ,3p • int. mass:QGP (resonances?)vs.cc → e+e-X (softening?) -