Heavy-Flavor Interactions in Medium Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, TX USA Workshop on Heavy-Quark Physics in Heavy-Ion Collisions ECT* (Trento, Italy),

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]

1.2 Objectives with Heavy Flavor in URHICs  Determine modifications of QCD force in medium + infer consequences for the many-body system Open heavy-flavor diffusion: Brownian motion - Scattering rates in QGP: widths, quasiparticles? (m Q  T) - Transport/thermalization: type of interaction (non/pert.,dofs, …) Quarkonia kinetics - Screening of confining (≥T c ?) + Coulomb (≥2T c ?) force - ϒ states: sequential melting - ψ states: sequential recombination

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

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

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

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

2.3.2 Free Energy from T-Matrix Key ingredients: imaginary parts + their  dependence heavy-quark selfenergies from 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]

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:

2.3.4 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

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

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

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+RR in prep]

3.3 D-Meson Transport in Hadronic Matter consistent with: - 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]

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 

| | 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]

3.6 Heavy-Flavor Electrons at √s=62GeV uncertainties in pp baseline interplay of Cronin (pA!) + collective flow sizable medium effects in R CP + v 2

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

4.) Charmonium:  (3686) easily dissociated in hadronic matter: , ,... +  →DD,  → D med D med [Grandchamp +RR ‘02 ] hadronic  dissociation at SPS important ingredient for transport models [Sorge et al ‘97, …] [PBM+Stachel ‘00]

4.2 Charmonia in d+Au Fireball construct fireball + evolve rate equat. →  suppression from hot medium similar in spirit to comover approach formation time effects?! [X.Du+RR, in prep ] [Ferreiro ‘14 ] [Y.Liu, Ko et al ‘14 ]

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

4.3.2 Sequential Recombination vs. Dissociation ψ blast wave fills p t = 3-6 GeV region, primordial for p t > 6 GeV helps explain CMS double-ratio puzzle more complex in practice … [X.Du+RR, in prep ] ψ / J/ψ Double Ratio R AA ψ / R AA J/ψ Nuclear Modification Factor

5.) Conclusions Heavy-quark potential in QGP from lQCD F: Bayesian, T-matrix - Large imaginary parts - Remnants of confinement generate strong coupling “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?! (↔ pA)

3.) 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

 c from fixed cc number: interplay of m c * and constrain spectral shape by lattice-QCD correlators 3.1 Thermal Charmonium Properties mc*mc* BB (a) Equilibrium  number: -  q (b) Inelastic  Width controlled by  s (parameter)

3.3 Inclusive J/  at SPS + RHIC Fix two main parameters:  s ~0.3, charm relax.  c eq = 4(2) fm/c for U(F) vs. ~5(10) from T-matrix Strong Binding (U) Weak Binding (F) [Zhao+RR ‘10]

3.4 J/  Excitation Function: BES at RHIC [Grandchamp +RR ’02 ] suppression pattern varies little (expected from transport) quantitative pp + pA baseline critical to extract systematics PHENIX (forward y) STAR (central y)

3.5 J/  Predictions at LHC regeneration becomes dominant uncertainties in  cc +shadowing [Zhao+RR ‘11 ] low p T maximum confirms regeneration too much high-p T suppression?

3.6  (1S) and  (2S) at LHC sensitive to color-screening + early evolution times clear preference for strong binding (U potential) similar results by possible problem in rapidity dependence  (1S) →  (2S) → [Grandchamp et al ’06, Emerick et al ‘11] Weak Binding Strong Binding [Strickland ‘12 ]

3.7 Summary of Phenomenology Quarkonium discoveries in URHICs: - increase of J/  R AA SPS, RHIC → LHC - low-p T enhancement - sizable v 2 - increasing suppression of  ’ (  B  ’ ~  B J/  ) Implications - T 0 SPS (~230) < T diss (J/ ,  ’) < T 0 RHIC (~350) < T 0 LHC (~550) ≤ T diss (  ) - confining force screened at RHIC+LHC - marked recombination of diffusing charm quarks at LHC Fair predictive power of theoretical modeling - based on description of SPS+RHIC with 2 main parameters

3.2.2 J/  at LHC: v 2 further increase at mid-y [He et al ’12 ]

3.1.2 J/  p T Spectra + Elliptic Flow at RHIC small v 2 limits regeneration, but does not exclude it (strong binding) shallow minimum at low p T high p T : formation time, b feeddown, Cronin

3.2.2 D-Meson Thermalization at LHC to be determined…

3.3.4 Time Evolution of J/  at LHC finite “cooking-time” window, determined by inelastic width [Zhao+RR ‘11 ] Strong Binding (U) Weak Binding (F)

4.3 J/  at Forward Rapidity at RHIC [Zhao+ RR ‘10]

3.2 Incomplete c-Quark Thermalization regeneration sensitive to charm-quark spectra [Song,Han, Ko ‘12 ] [Zhao+RR ‘11] Relaxation time ansatz: N  eq (  ) ~ N  therm (  ) · [1-exp(-  /  c eq )] Microscopic Calculation Impact on Regeneration

3.6.1 Heavy-Flavor Electrons at √s=62GeV importance of flow + Cronin effect at lower energies Hydro Tune