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Nonperturbative Heavy-Quark Interactions in the QGP

Nonperturbative Heavy-Quark Interactions in the QGP. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: F. Riek (Texas A&M), H. van Hees (Giessen), V. Greco (Catania), M. Mannarelli (Barcelona). 1.) Introduction.

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Nonperturbative Heavy-Quark Interactions in the QGP

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  1. Nonperturbative Heavy-Quark Interactions in the QGP Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: F. Riek (Texas A&M), H. van Hees (Giessen), V. Greco (Catania), M. Mannarelli (Barcelona)

  2. 1.) Introduction • “Large” scale mQ >> LQCD , T • Low-energy/-momentum interactions: • - heavy-quark diffusion ↔ elastic scattering, Fokker-Planck • - quarkonia ↔ potential QCD • → uniform framework • as expansion inadequate • → resummations, bound + scattering states • theo. / pheno. constraints essential • (baselines prior to applications in heavy-ion collisions)

  3. Outline 1.) Introduction 2.) T-Matrix Approach with Heavy Quarks  Potential Approach + Lippmann Schwinger Eq.  Vacuum and pQCD Limits  In-Medium Potentials  Q-Q and Q-q Scattering in Medium 3.) Heavy-Quark Diffusion in QGP  Fokker-Planck Equation  Transport coefficients  Electron Spectra at RHIC 4.) Conclusions

  4. 2.) T-Matrix Approach with Heavy Quarks • HQ potential concept well established • in vacuum (EFT, lattice) • 3-D reduction of Bethe-Salpeter Eq. Lippmann-Schwinger Equation [Mannarelli+RR ’05, Cabrera+RR ‘06] In-Medium Q-QT-Matrix: - - - Q-Q propagator: - bound + scattering states • 2-body potential VL in medium?Color-Magnetic Interaction?

  5. 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)

  6. 2.3 Lattice QCD Free Energy + In-Medium Potential • F1(r,T) = U1(r,T) – T S1(r,T) • V1(r,T) ≡ X1(r,T) - X1(r=∞,T) • (X1∞ / 2 : in-medium quark-mass?!) • (a) X1=F1 : trelax << tint • (b) X1=U1 : trelax >> tint • (c) Landau-Zener “mixing” • X1 = P U1 + (1-P) F1 • P = exp[- 2p |H12|2 / vrel d/dr (F1-U1)] • |H12| ~ 1/trelax [Shuryak ‘08, Riek et al ‘09] [Kaczmarek +Zantow ’05]

  7. 2.4 Charmonium T-Matrix in QGP • ground state bound to ~ 2 Tc for V = U, VLZ • ~ 1.2Tc for V = F

  8. 2.5 Heavy-Light Quark Scattering in QGP • threshold S-wave resonances (meson+diquark) close to TC

  9. 3.) Heavy-Quark Transport in the QGP • Brownian • Motion: Fokker Planck Eq. Q [Svetitsky ’88,…] thermalization rate diffusion coefficient • Transition rate: wQ(p,k) ~ ∑ q,g ∫ fq,g(E;T) |TQq|2 • Heavy-quark selfenergy: Q

  10. 3.2 Charm-Quark Selfenergy + Drag Selfenergy Thermalization Rate • charm quark widths Gc = -2 ImSc ~ 250 MeV close to TC • friction coefficients increase(!) with decreasing T→TC!

  11. 3.3 Comparison of Drag Coefficients(Thermal Relaxation Rate) [Gubser ’06] [Peshier ‘06; Gossiaux+Aichelin ’08] g [1/fm] [van Hees+RR ’04] [van Hees,Mannarelli, Greco+RR ’07] T [GeV] • T-matrix rate ~ constant (melting resonances) • trelax = 1/g ~ 7 fm/c

  12. 3.4 T-Matrix Approach vs. e± Spectra at RHIC [van Hees,Mannarelli,Greco+RR ’07] • max. interaction at~Tc • ↔ hadronic correlations • ↔ quark coalescence Spatial Diffusion Coeff.

  13. 4.) Summary and Conclusions • In-MediumQ-q+Q-QT-Matrix • → heavy-quark diffusion and quarkonia in QGP on same footing • Constraints essential: • - lQCD based potential (F-U relaxation), Eucl. correlators • - vacuum, pQCD • “hadronic” correlations close to Tc ↔ quark coalescence • ↔ max. coupling strength at ~Tc ↔ min. h/s !? • Radiative diffusion? Light-quark sector? Non-pert. gluons? … • RHIC non-photonic e± Ds (2pT) ≈ 5 • - v2 - RAA correlation essential • - scrutinize medium evolution, Fokker-Planck, d-Au …

  14. 3.1 HQ Langevin Simulations: Hydro vs. Fireball Elastic pQCD + Hydrodynamics [Moore+Teaney ’05] • b=6.5 fm • Tc=165 MeV • t ≈ 9 fm/c Ds (2pT) ≈ 6  v2max ~ 5-6% RAA~ 0.3 Resonance Model + Expanding Fireball • Tc=180 MeV • bulk-v2 ~5.5% • tQGP ≈ 5 fm/c [van Hees,Greco +RR ’05]

  15. 2.3 AdS/CFT-QCD Correspondence 3-momentum independent [Herzog et al, Gubser ‘06] • match energy density • (d.o.f = 120 vs. ~40) • and coupling constant • (heavy-quark potential) • to QCD Lat-QCD TQCD ~ 250 MeV  ≈ (4-2 fm/c)-1 at T=180-250 MeV [Gubser ‘07]

  16. 3.) Phenomenology at RHIC • Medium evolution • - hydrodynamics or parameterizations thereof • - realistic bulk-v2(~5-6%) • - stop evolution after QGP; hadronic phase? • Hadronization • - fragmentation: c → D + X • - coalescence: c + q → D, adds momentum and v2 • - chemistry (e.g. Lc enhancement) • Semileptonic electron decays • - approx. conserve v2 and RAA 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]

  17. 3.3 Heavy-Quark Spectra at RHIC • relativistic Langevin simulation in thermal fireball background Nuclear Modification Factor Elliptic Flow pT [GeV] pT [GeV] • T-matrix approach ≈ effective resonance model • other mechanisms: radiative (2↔3), … [Wiedemann et al.’05,Wicks et al.’06, Vitev et al.’06, Ko et al.’06]

  18. 4.) Maximal “Interaction Strength” in the sQGP • potential-based description ↔ strongest interactions close to Tc • - consistent with minimum in h/s at ~Tc • - strong hadronic correlations at Tc ↔ quark coalescence • semi-quantitative estimate for diffusion constant: weak coupl. h/s ≈ 4/15 n <p> ltr=1/5 T Ds strong coupl. h/s≈ 1/4p Ds(2pT) = 1/2 T Ds  h/s≈ (2-4)/4p close toTc [Lacey et al. ’06]

  19. 3.2.2 The first 5 fm/c for Charm-Quark v2 + RAA Inclusive v2 Time Evolution • RAA built up earlier than v2

  20. 2.2.2 “Lattice QCD-based” Potentials • accurate lattice “data” for free energy:F1(r,T) = U1(r,T) – T S1(r,T) • V1(r,T) ≡ U1(r,T) - U1(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]

  21. 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

  22. 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?!

  23. 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!

  24. 3.2 Model Predictions vs. PHENIX Data Single-e±Spectra [PHENIX ’06] • pQCD radiative E-loss with • upscaled transport coeff. • Langevin with elastic pQCD + • resonances + coalescence • Langevin with upscaled • pQCD elastic • coalescence increases • bothRAA and v2

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