HeavyFlavor Interactions in Medium Ralf Rapp Cyclotron Institute

Heavy-Flavor Interactions in Medium Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, TX USA 6 th Workshop of the APS Topical Group on Hadronic Physics Baltimore (MD), 08. -10. 04. 15

1. ) Introduction: A “Calibrated” QCD Force V [½ Ge. V] r [½ fm] • Vacuum charm-/bottomonium spectroscopy well described • Confinement ↔ linear part of potential • non-perturbative treatment in medium lattice QCD, potential / T-matrix approach, Ad. S/CFT, … [Kaczmarek et al ‘ 03]

1. 2 Objectives with Heavy Flavor in URHICs Determine modifications of QCD force in medium + infer consequences for the many-body system • exploit m. Q >> LQCD , Tc , T(RHIC, LHC) • Open heavy-flavor diffusion: “Brownian markers of QGP” - Scattering rates: widths, quasiparticles? (m. Q T) - Thermalization: delayed by m. Q/T → memory - Transport: diffusion coefficient Ds (2πT) ~ η/s • Quarkonia kinetics - Screening of confining (≥Tc? ) + Coulomb (≥ 2 Tc? ) force - ϒ states: sequential melting - ψ states: (sequential? ) regeneration

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

2. 1 Free + Internal Energy from Lattice QCD F 1(r, T) = U 1(r, T) – T Free Energy. S 1(r, T) Internal Energy • marked gradual “screening” • U = ‹Hint› • non-trivial many-body correlations • F, U, S thermodynamic quantities • Underlying ``bare” interaction?

2. 2 Thermodynamic T-Matrix in QGP • Lippmann-Schwinger equation In-Medium Q-Q T-Matrix: • thermal 2 -particle propagator: q, g • selfenergy: SQ = • rooted in vacuum spectroscopy; recovers p. QCD at large q 2 • in-medium potential V? [Cabrera+RR ’ 06, Riek+RR ‘ 10]

2. 2. 2 Free Energy from T-Matrix • Free Energy • Euclidean T-matrix in static limit • Spectral Function • Key ingredients: imaginary parts + their w dependence • heavy-quark selfenergies (from heavy-light T-matrix) [Beraudo et al ’ 08] [S. Liu+RR in progress] [S. Liu+RR ’ 15]

2. 2. 3. Free + Internal Energy from T-Matrix • field-theoretic potential ansatz: [Megias et al ’ 07] lattice data U V F 1. 2 Tc r [fm] 1. 5 Tc r [fm] 2 Tc r [fm] • remnant of long-range “confining” force in QGP

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

3. 1 Heavy-Light Interactions in QGP c-q- Thermal Relaxation Rate gc [1/fm] T-Matrix p [Ge. V] • (pre-) resonances close to Tc • same interaction for transport + hadronization • • tc ≈ 3 fm/c close to Tc at low p • transition non-pert → pert. QCD

3. 2 Charm Diffusion Coefficient in Matter Ds =T/m. Qg. Q : Hadronic Matter vs. QGP vs. Lattice QCD [He et al ’ 11, Riek+RR ’ 10, Ding et al ‘ 11, Gavai et al ‘ 11] Ad. S/QCD • shallow minimum near Tc • Quark-Hadron continuity? [Gubser ‘ 07]

3. 3 Heavy-Flavor Transport in URHICs 0 | 0. 5 | t [fm/c] 5 | D c • initial cond. (shadowing, • c-quark diffusion Cronin), in QGP liquid pre-equil. fields 10 | • c-quark hadronization • D-meson diffusion in hadron liquid • no “discontinuities” in interaction diffusion toward Tpc and hadronization same interaction (confining!)

5. ) Charm Transport in Heavy-Ion Collisions [M. He et al ’ 14] • RAA “bump” from radial flow • Ds meson (cs) enhanced from coalescence with strange quarks • Coalescence + hadronic diffusion increase v 2 • similar features at RHIC

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

4. ) Quarkonium Transport in Heavy-Ion Collisions • Inelastic Reactions: [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, …] → c + c- + X detailed balance: J/y + g ← • Rate Equation: D - D J/y c- c J/y • Transport coefficients - chemical relaxation rate Gy - equililbrium limit Nyeq(ey. B, mc* , tceq) • Phenomenology: - J/y, cc, y’+c, b initial distributions [pp, p. A] - medium evolution [AA: hydro, . . . ] Observables

4. 2 J/y Predictions at LHC • regeneration becomes dominant • uncertainties in scc+ shadowing • maximum at low pt corroborates regeneration [Zhao+RR ‘ 11]

4. 3. 1 Time Evolution of Charmonia in the Fireball Time Evolution Momentum Spectra • smaller binding → smaller Tdiss → y forms later than J/ψ ! • stronger fireball expansion for ψ → harder pt spectra (slope parameter Teff ~ T + m b┴ 2 ) [X. Du+RR ‘ 15]

4. 3. 2 Sequential Recombination + CMS Data ψ’ / J/ψ RAA Double Ratio • ψ blast wave fills pt = 3 -6 Ge. V region, primordial for pt > 6 Ge. V • helps explain CMS double-ratio “puzzle” [X. Du+RR ‘ 15]

5. ) Conclusions • Extract heavy-quark potential in QGP from lat-QCD free energy: - Large imaginary parts - Remnants of confinement generate strong coupling • “Critical” consequences for heavy-flavor diffusion: Continuity + minimum of transport coefficient through Tpc • Diffusion + hadronization from same interaction • Sequential recombination of charmonia? !

2. 2. 4 Brueckner Theory of Heavy Flavor in QGP Input lattice-QCD free energy 2 -body potential Quark selfenergy Process Q→Q 0 -modes - QQ T-matrix Qq T-matrix Output Test quark-no. susceptibility spectral fcts. / eucl. correlat. lattice data - evolution QQ (rate equation) exp. data Q spectra + v 2 (Langevin)

4. 2 Charmonia in d+Au Fireball • construct fireball + evolve rate equat. → y suppression from hot medium • similar in spirit to comover approach [Ferreiro ‘ 14] • formation time effects? ! [X. Du+RR, in prep] [Y. Liu, Ko et al ‘ 14]

4. ) Charmonium: y (3686) • easily dissociated in hadronic matter: p, r, . . . + y →DD, y → Dmed [Grandchamp +RR ‘ 02] [PBM+Stachel ‘ 00] • hadronic y dissociation at SPS important ingredient for transport models [Sorge et al ‘ 97, …]

3. 6 (1 S) and (2 S) at LHC Weak Binding Strong Binding (1 S) → (2 S) → [Grandchamp et al ’ 06, Emerick et al ‘ 11] • sensitive to color-screening + early evolution times • clear preference for strong binding (U potential) • similar results by [Strickland ‘ 12] • possible problem in rapidity dependence

3. 3 D-Meson Transport in Hadronic Matter g. D [fm-1] • effective D-h scattering amplitudes [He, Fries+RR ’ 11] • consistent with: - unitarized HQET (pion gas) [Cabrera et al ‘ 11] - recent works in HRG using similar methods [Tolos+Torres-Ricon ’ 13, Ozvenchuk et al ‘ 14] g. D [fm-1] • hadron gas at ~Tc: t. D ≈ 10 fm/c

3. 1 Thermal Charmonium Properties (a) Equilibrium Y number: • gc from fixed cc- number: • interplay of mc* and • constrain spectral shape by lattice-QCD correlators (b) Inelastic Y Width e y. B mc * q q • controlled by as (parameter) Gy

3. 3 Inclusive J/y at SPS + RHIC Strong Binding (U) Weak Binding (F) [Zhao+RR ‘ 10] • Fix two main parameters: as~0. 3, charm relax. tceq = 4(2) fm/c for U(F) vs. ~5(10) from T-matrix

3. 4 J/y Excitation Function: BES at RHIC PHENIX (forward y) STAR (central y) • suppression pattern varies little (expected from transport) [Grandchamp +RR ’ 02] • quantitative pp + p. A baseline critical to extract systematics

3. 5 J/y Predictions at LHC [Zhao+RR ‘ 11] • regeneration becomes dominant • uncertainties in scc+shadowing • low p. T maximum confirms regeneration • too much high-p. T suppression?

3. 7 Summary of Phenomenology • Quarkonium discoveries in URHICs: - increase of J/y RAA SPS, RHIC → LHC - low-p. T enhancement - sizable v 2 - increasing suppression of ’ (e. B ’ ~ e. BJ/y ) • Fair predictive power of theoretical modeling - based on description of SPS+RHIC with 2 main parameters • Implications - T 0 SPS (~230) < Tdiss(J/y, ’) < T 0 RHIC (~350) < T 0 LHC(~550) ≤ Tdiss( ) - confining force screened at RHIC+LHC - marked recombination of diffusing charm quarks at LHC

3. 2. 2 J/y at LHC: v 2 [He et al ’ 12] • further increase at mid-y

3. 1. 2 J/y p. T Spectra + Elliptic Flow at RHIC (strong binding) • shallow minimum at low p. T • high p. T: formation time, b feeddown, Cronin • small v 2 limits regeneration, but does not exclude it

3. 2. 2 D-Meson Thermalization at LHC • to be determined…