1. Interactions of Heavy Flavor in Medium Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, TX USA Kavli Institute of Theoretical Physics China Program on “sQGP and extreme QCD” CAS (Beijing, China), 26.05.15

2. 1.) Introduction: A “Calibrated” QCD Force  Vacuum charm-/bottomonium spectroscopy well described Confinement ↔ linear part of potential non-perturbative treatment in medium lattice QCD, potential/T-matrix approach, AdS/CFT, … relate quarkonia kinetics and heavy-flavor diffusion [Kaczmarek et al ‘03] V [½ GeV] r [½ fm]

3. strong medium effects, nonpert.: F(r) > 0 for T ≤ 2T c momentum transfer single heavy quark in QGP 1.2 Intro II: Heavy-Quark Interactions in Medium Q QGP soft Q-Q and Q-medium interactions quasi-static + elastic  common treatment of quarkonia + heavy-quark transport bound + scattering states, resummations  thermodynamic T-matrix approach (e.m. plasmas, nucl. matter) - Q Free Energy

4. 1.) Introduction 2.) Heavy-Quark Interactions in QGP 3.) Open Heavy-Flavor Transport 4.) Quarkonia: ψ Puzzle(s) 5.) Conclusions Outline

5. 2.1 Free and Internal Energy in Lattice QCD “strong” QQ potential, U = ‹H int › large  m Q ~ U 1 (∞,T)/2 - - F 1 (r,T) = U 1 (r,T) – T S 1 (r,T) “weak” QQ potential small  m Q ~ F 1 (∞,T)/2 F, U, S thermodynamic quantities Entropy: many-body effects Free Energy Internal Energy

6. 2.2 Reconstructed Potential from Lattice QCD real part ~ singlet free energy imaginary part ~ HTL perturbative Real Part Imaginary Part [Burnier et al ’14] static potential from Wilson loop correlator:

7. Lippmann-Schwinger equation In-Medium Q-Q T-Matrix: - 2.3 Thermodynamic T-Matrix in QGP thermal 2-particle propagator: selfenergy: In-medium potential V? QQ q,g = [Cabrera+RR ’06, Riek+RR ‘10]

8. 2.4 Free Energy from T-Matrix Weak coupling: V QQ → F QQ Key ingredients: - imaginary parts + their  dependence - heavy-quark selfenergies (previous T-matrix calculations) [S.Liu+RR in progress ] Euclidean T-matrix in static limit Spectral Function Free Energy [S.Liu+RR ’15] [Beraudo et al ’08]

9. 2.4.2 Free + Internal Energy from T-Matrix remnant of long-range “confining” force in QGP smaller in-medium quark mass relative to internal energy 1.2 T c 1.5 T c 2 T c U F V lattice data r [fm] potential ansatz: [Megias et al. ’07]

10. 2.5 Brueckner Theory of Heavy Flavor in QGP 2-body potential QQ T-matrix Qq T-matrix Q → Q 0-modes Quark selfenergy QQ evolution (rate equation) Q spectra + v 2 (Langevin) spectral fcts./ eucl. correlat. quark-no. susceptibility lattice data exp. data Input Process Output Test - - lattice-QCD free energy

11. 2.6 Quarkonium Correlators + Spectral Functions Euclidean Correlation Function Correlator Ratio: Spectral Function Relation: [Datta et al ‘04] cc J/  [Asakawa et al ’03, Iida et al ’06, Aarts et al ‘07, Jakovac et al ’07,…] → Lattice QCD!

12. U-potential, selfconsist. c-quark width Spectral Functions - J/  melting at ~1.5T c -  c melting at ~T c -  c ~ 200MeV Correlator Ratios - rough agreement with lattice-QCD 2.6.2 Charmonia in QGP from T-Matrix [Mocsy+ Petreczky ’05+’08, Wong ’06, Cabrera+RR ’06, Beraudo et al ’06, Satz et al ’08, Lee et al ’09, Riek+RR ’10, …] [Aarts et al ‘07]

13. 2.6.3 Charm-Quark Susceptibility in QGP sensitive to in-medium charm-quark mass finite-width effects can compensate in-medium mass increase [Riek+RR ‘10] 2 → →  → 0 m « T

14. 1.) Introduction 2.) Heavy-Quark Interactions in QGP 3.) Open Heavy-Flavor Transport 4.) Quarkonia: ψ Puzzle(s) 5.) Conclusions Outline

15. 3.1 Heavy-Light Scattering Amplitudes “confining” force induces “Feshbach resonances” in Qq T-matrix strength comparable to internal-energy (U) potential c-q - New Potential V U-Potential

16. 3.2 Charm-Quark Relaxation Rates heavy-light T-matrix → HQ transport:  c  [1/fm]  c ≈ 3 fm/c close to T c at low p 3-mom. + temperature dependence reflect core properties of QCD! Relaxation Rate Diffusion Coefficient p [GeV] [S.Liu,M.He +RR in prep]

17. 3.3 D-Meson Transport in Hadronic Matter also found by: - unitarized HQET (pion gas) - recent works in HRG using similar methods effective D-h scattering amplitudes [He,Fries+RR ’11]  D  [fm -1 ] [Cabrera et al ‘11] hadron gas at ~T c :  D ≈ 10fm/c  D  [fm -1 ] [Tolos+Torres-Ricon ’13, Ozvenchuk et al ‘14]

18. 3.4 Summary of Charm Diffusion in Matter shallow minimum near T c Quark-Hadron continuity?  Hadronic Matter vs. QGP vs. Lattice QCD [He et al ’11, Riek+RR ’10, Ding et al ‘11, Gavai et al ‘11] AdS/QCD [Gubser ‘07] D s =T/m 

19. | | 3.5 Heavy-Flavor Transport in URHICs no “discontinuities” in interaction  diffusion toward T pc and hadronization same interaction (confining!) initial cond. (shadowing, Cronin), pre-equil. fields c-quark diffusion in QGP liquid c-quark hadronization D-meson diffusion in hadron liquid  c D  [fm/c] 0 0.5 5 10

20. 1.) Introduction 2.) Heavy-Quark Interactions in QGP 3.) Open Heavy-Flavor Transport 4.) Quarkonia: ψ Puzzle(s) 5.) Conclusions Outline

21. 4.) Quarkonium Transport in Heavy-Ion Collisions J/  D D - c - c [PBM+Stachel ’00,Thews et al ’01, Grandchamp+RR ‘01, Gorenstein et al ’02, Ko et al ’02, Andronic et al ‘03, Zhuang et al ’05, Ferreiro et al ‘11, …] J/  + g c + c + X ← → - Inelastic reactions: detailed balance: Theoretical input: transport coefficients - chemical relaxation rate   - equililbrium limit N  eq (   B, m c *,  c eq ) Phenomenological input: - J/ ,  c,  ’+c,b initial distributions [pp, pA] - space-time medium evolution [AA: hydro,...] Rate equation: Observables

22. 4.2 Excited Charmonium:  (3686) easily dissociated in hadronic matter: , ,... +  →DD,  → D med D med hadronic  dissociation at SPS important in transport models [Sorge et al ‘97, Grandchamp et al.…] [PBM+ Stachel ‘00] NA50 @ SPS (√s=17.3GeV) CMS @ LHC (√s=2.76TeV)  enhanced relative to J/  ?!

23. 4.3 Sequential Recombination of Charmonia in AA smaller binding → smaller T diss →  forms later than J/ψ ! stronger blast wave for ψ formed at later times (hadronic phase!) [X.Du+RR ‘15 ] Time Evolution p T Spectra

24. 4.3.2 Sequential Recombination vs. Dissociation ψ blast wave fills p t = 3-6 GeV region, primordial for p t > 6 GeV may help explain CMS double-ratio puzzle … [X.Du+RR ‘15 ] ψ / J/ψ Double Ratio R AA ψ / R AA J/ψ Nuclear Modification Factor

25. 5.) Summary Heavy-quark potential in QGP from lattice-F: Bayesian, T-matrix - Large imaginary parts - Remnants of confinement generate strong coupling T-Matrix approach to bridge lattice and phenomenology “Critical” consequences for heavy-flavor diffusion Continuity(?) + minimum of transport coefficient through T pc No principal difference between diffusion forces + hadronization Sequential recombination of charmonia?