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Heavy-Flavor Interactions in Medium

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), 16.-20.03.15.

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Heavy-Flavor Interactions in Medium

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  1. 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), 16.-20.03.15

  2. 1.) Introduction: A “Calibrated” QCD Force V [½GeV] [Kaczmarek et al ‘03] 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, AdS/CFT, … • relate quarkonia kinetics and heavy-flavor diffusion

  3. 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? (mQT) • - Transport/thermalization: type of interaction (non/pert.,dofs,…) • Quarkonia kinetics • - Screening of confining (≥Tc?) + Coulomb (≥2Tc?) force • - ϒ states: sequential melting • - ψ states: sequential recombination

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

  5. 2.1 Free and Internal Energy in Lattice QCD F1(r,T) = U1(r,T) – T S1(r,T) Free Energy Internal Energy - - • “strong”QQ potential,U = ‹Hint› • large DmQ ~ U1(∞,T)/2 • “weak”QQ potential • small DmQ~ F1(∞,T)/2 • F, U, Sthermodynamic quantities • Entropy: many-body effects

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

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

  8. 2.3.2 Free Energy from T-Matrix • Free Energy [Beraudo et al ’08] • Euclidean T-matrix in static limit [S.Liu+RR in progress] • Spectral Function [S.Liu+RR ’15] • Key ingredients: imaginary parts + their w dependence • heavy-quark selfenergies from previous T-matrix calculations

  9. 2.3.3. Free + Internal Energy from T-Matrix • potential ansatz: U V F lattice data 1.2 Tc 1.5 Tc 2 Tc r [fm] r [fm] r [fm] • remnant of long-range “confining” force in QGP • smaller in-medium quark mass relative to internal energy

  10. 2.3.4 Brueckner Theory of Heavy Flavor in QGP InputProcessOutputTest quark-no. susceptibility lattice-QCD free energy Q → Q 0-modes lattice data spectral fcts./ eucl. correlat. - 2-body potential QQ T-matrix - QQ evolution (rate equation) Qq T-matrix Quark selfenergy exp. data Q spectra + v2 (Langevin)

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

  12. 3.1 Heavy-Light Scattering Amplitudes New Potential VU-Potential - c-q • “confining” force induces “Feshbach resonances” in QqT-matrix • strength comparable to internal-energy (U) potential

  13. 3.2 Charm-Quark Relaxation Rates • heavy-light T-matrix → HQ transport: Relaxation Rate Diffusion Coefficient gc[1/fm] p [GeV] [S.Liu+RR in prep] • tc ≈ 3 fm/c close to Tc at low p • 3-mom. + temperature dependence reflect core properties of QCD!

  14. 3.3 D-Meson Transport in Hadronic Matter gD[fm-1] • effective D-h scattering amplitudes [He,Fries+RR ’11] • hadron gas at ~Tc: tD≈ 10fm/c • consistent with: • - unitarized HQET (pion gas) • - recent works in HRG using similar • methods [Cabrera et al ‘11] [Tolos+Torres-Ricon ’13, Ozvenchuk et al ‘14] gD[fm-1]

  15. 3.4 Summary of Charm Diffusion in Matter Ds=T/mg : 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] • shallow minimum near Tc • Quark-Hadron continuity?

  16. 3.5 Heavy-Flavor Transport in URHICs 0 0.5 5 10 | | | | t [fm/c] D c • initial cond. • (shadowing, • Cronin), • pre-equil. fields • c-quark diffusion • in QGP liquid • c-quark • hadronization • D-meson • diffusion in • hadron liquid • no “discontinuities” in interaction • diffusion toward Tpcand hadronization same interaction (confining!)

  17. 3.6 Heavy-Flavor Electrons at √s=62GeV • uncertainties in pp baseline • interplay of Cronin (pA!) + collective flow • sizable medium effects in RCP + v2

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

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

  20. 4.2 Charmonia in d+Au Fireball • construct fireball + evolve rate equat. → y suppression from hot medium • similar in spirit to comover approach • formation time effects?! [Ferreiro ‘14] [X.Du+RR, in prep] [Y.Liu, Ko et al ‘14]

  21. 4.3.1 Sequential Recombination of Charmonia in AA Time Evolution pT Spectra • smaller binding → smaller Tdiss→ y forms later than J/ψ! • harder blast wave for ψformed at later times (hadronic phase!) [X.Du+RR, in prep]

  22. 4.3.2 Sequential Recombination vs. Dissociation ψ / J/ψDouble Ratio Nuclear Modification Factor RAA ψ / RAA J/ψ • ψblast wave fills pt = 3-6 GeV region, primordial for pt > 6 GeV • helps explain CMS double-ratio puzzle • more complex in practice … [X.Du+RR, in prep]

  23. 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 Tpc • No principal difference between diffusion forces + hadronization • Sequential recombination of charmonia?! (↔ pA)

  24. D - D J/y - c c J/y 3.) Quarkonium Transport in Heavy-Ion Collisions [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, …] • Inelastic Reactions: detailed balance: → - ← J/y + g c + c + X • Rate • Equation: • Theoretical Input: Transport coefficients • - chemical relaxation rate Gy • - equililbrium limit Nyeq(eyB, mc* ,tceq) • Phenomenological Input: • - J/y,cc,y’+c,b initial distributions [pp, pA] • - space-time medium evolution [AA: hydro,...] Observables

  25. 3.1 Thermal Charmonium Properties (a) EquilibriumYnumber: - • gc from fixed cc number: • interplay of mc* and • constrain spectral shape by lattice-QCD correlators eyB mc* (b) Inelastic YWidth q q • controlled by as(parameter) Gy

  26. 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

  27. 3.4 J/y Excitation Function: BES at RHIC PHENIX (forward y) STAR (central y) [Grandchamp +RR ’02] • suppression pattern varies little (expected from transport) • quantitative pp + pA baseline critical to extract systematics

  28. 3.5 J/y Predictions at LHC [Zhao+RR ‘11] • regeneration becomes dominant • uncertainties in scc+shadowing • low pT maximum confirms regeneration • too much high-pT suppression?

  29. 3.6 (1S) and (2S) at LHC Weak Binding Strong Binding (1S) → (2S) → • sensitive to color-screening + early evolution times • clear preference for strong binding (U potential) • similar results by • possible problem in rapidity dependence [Grandchamp et al ’06, Emerick et al ‘11] [Strickland ‘12]

  30. 3.7 Summary of Phenomenology • Quarkonium discoveries in URHICs: • - increase of J/yRAASPS, RHIC → LHC • - low-pT enhancement • - sizable v2 • - increasing suppression of ’ (eB’~ eBJ/y) • Fair predictive power of theoretical modeling - based on description of SPS+RHIC with 2 main parameters • Implications - T0 SPS(~230) < Tdiss(J/y,’) < T0RHIC (~350) < T0LHC(~550) ≤ Tdiss() - confining force screened at RHIC+LHC - marked recombination of diffusing charm quarks at LHC

  31. 3.2.2 J/y at LHC: v2 [He et al ’12] • further increase at mid-y

  32. 3.1.2 J/y pT Spectra + Elliptic Flow at RHIC (strong binding) • shallow minimum at low pT • high pT: formation time, b feeddown, Cronin • small v2limits regeneration, but does not exclude it

  33. 3.2.2 D-Meson Thermalization at LHC • to be determined…

  34. 3.3.4 Time Evolution of J/y at LHC Strong Binding (U) Weak Binding (F) • finite “cooking-time” window, determined by inelastic width [Zhao+RR ‘11]

  35. 4.3 J/y at Forward Rapidity at RHIC [Zhao+ RR ‘10]

  36. 3.2 Incomplete c-Quark Thermalization • Relaxation time ansatz: Nyeq (t) ~ Nytherm(t) · [1-exp(-t/tceq)] Microscopic Calculation Impact on Regeneration [Zhao+RR ‘11] [Song,Han, Ko ‘12] • regeneration sensitive to charm-quark spectra

  37. 3.6.1 Heavy-Flavor Electrons at √s=62GeV Hydro Tune • importance of flow + Cronin effect • at lower energies

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