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From Heavy-Flavor Transport to Bulk and Spectral Properties of the QGP

From Heavy-Flavor Transport to Bulk and Spectral Properties of the QGP. Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, TX, USA + EMMI (GSI, Darmstadt, GER) HIC for FAIR Nuclear Physics Colloquium

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From Heavy-Flavor Transport to Bulk and Spectral Properties of the QGP

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  1. From Heavy-Flavor Transport to Bulk and Spectral Properties of the QGP Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, TX, USA + EMMI (GSI, Darmstadt, GER) HIC forFAIR Nuclear Physics Colloquium Frankfurt University (Germany) June 14, 2018

  2. 1.) Heavy Quarks: A “Calibrated” QCD Force [GeV] V [½GeV] r [½ fm] [Bazavov et al ‘13] • Vacuum quarkonium spectroscopy well described • Confinement ↔ linear part of potential Objective: Determine medium-modifications of QCD force  deduce transport properties + spectral functions of heavy flavor, probing QGP at varying resolution Exploit mQ >> LQCD , Tc , TRHIC,LHC

  3. 1.2 Quarkonia in Medium • In-medium spectral functions: • - Mass / binding energy EB(p,T) • - Inelastic reaction rate Gin(p,T,EB) • (dissociation and regeneration) • (1S): color-Coulomb force • J/y, (2S), …: confining force • How do heavy quarks within quarkonia • interact with the medium? • Not a good thermometer…

  4. 1.3 Heavy Quarks in Medium • Diffusion: “Brownian motion” • Thermalizationdelayed by mQ/T • → memory in URHICs • Direct access to transport coefficient • Ds (2πT) (~ η/s ~ sEM/T !?) • Scattering rates • → widths (quantum effects); quasiparticles? (mQT) • → simple estimate: Ds(2pT)=3  GQ ~1GeV • - Implications for QGP structure? • Non-perturbative effects • Probe of hadronization (Ds, Lc) Q QGP Q

  5. Outline 1.) Introduction 2.) Quarkonia ●Transport Coefficients ●Phenomenology 3.) Open Heavy Flavor ●Brownian Motion of Heavy Quarks ●Phenomenology 4.) Many-Body Theory of Heavy Quarks + QGP ●T-Matrix Approach ●QGP Properties 5.) Conclusions

  6. q q D - D J/y - c c J/y 2.1 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: • Transport coefficients • - Equilibrium limit Nyeq(my,T; Ncc) - Reaction Rate Gy (EB(T)) “Weak” binding EB< mD “Strong” binding EB≥ T • “quasi-free”/ Landau damping • gluo-dissosciation (“singlet-to-octet”)

  7. 2.2 Excitation Functions: SPS - RHIC - LHC Charmonium Bottomonium • Gradual increase of total J/yRAA • Regeneration and suppression increase • Regeneration concentrated at low pT! [data: NA50, PHENIX, STAR, ALICE, CMS] • Gradual suppression • Regeneration (Nϒeq) small • Qualitative difference from J/y

  8. 2.3 Upshot of Quarkonium Phenomenology Use temperature estimates from hydro/photons/dileptonsto infer: T0SPS(~240)<Tmelt(J/y,)≤T0RHIC (~350)<Tmelt()≤T0LHC (~550) • Remnants of confining force survive at SPS[hold J/y together] • Confining force screened atRHIC+LHC [“melts” J/y+(2S)] • Color-Coulomb screening at LHC[(1S) suppression] • Thermalizing charm quarks recombine at LHC[large J/y yield] 1.5 1 0.5 0 -0.5 -1 r [fm] 0.25 0.5 0.75 1 1.25 1.5 350 240 550 (2S) J/, (2S) (1S)

  9. Outline 1.) Introduction 2.) Quarkonia ●Transport Coefficients ●Phenomenology 3.) Open Heavy Flavor ●Brownian Motion of Heavy Quarks ●Phenomenology 4.) Many-Body Theory of Heavy Quarks + QGP ●T-Matrix Approach ●QGP Properties 5.) Conclusions

  10. 3.1 Heavy-Flavor Transport in URHICs 0 0.5 5 10 | | | | t [fm/c] D c • initial cond. (nPDFs, …), 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!) [Moore+Teaney ‘05, van Hees et al ‘05, Gossiaux et al ‘08, Vitev et al ‘08, Das et al ‘09, Uphoff et al ’10, M.He et al ‘11, Beraudo et al ‘11, Cao et al ’13, Bratkovskaya et al ‘14, …]

  11. 3.2 Heavy-Flavor Transport • p2 ~ mQ T>> q2 ~ T2Brownian Motion: Fokker- Planck Q thermalization rate diffusion coefficient Dp =  d3q wQ(q,p) q2 g p =  d3q wQ(q,p) q ~  |TQj|2 (1-cosq) f j • thermal relaxation time tQ = 1/g • Einstein relation: T = Dp / g mQ • spatial diffusion constant: Ds = T/gmQ , <x2> - <x>2 = 6 Ds t • relation to bulk medium: Ds (2pT) ~ h/s (4π)

  12. 3.3 Heavy-Flavor Phenomemology at RHIC + LHC • Flow bump in RAA +large v2↔ strong coupling near Tpc (recombination) • Importance of T- + p-dependence of transport; Ds(2πT) ~ 2-4 near Tpc • High-precision v2: transition from elastic to radiative regime

  13. 3.4 Spatial Charm-Quark Diffusion Coefficient Ds= T/ (mQgQ(p=0)) HICs T/Tc • suggests minimum of Ds(2pT) ~ 2-5 near Tpc • width: Gcoll ~ 3/Ds ~ 1 GeV -no light quasi-particles! • upper limit from heavy-ion phenomenology

  14. Outline 1.) Introduction 2.) Quarkonia ●Transport Coefficients ●Phenomenology 3.) Open Heavy Flavor ●Brownian Motion of Heavy Quarks ●Phenomenology 4.) Many-Body Theory of Heavy Quarks + QGP ●T-Matrix Approach ●QGP Properties 5.) Conclusions

  15. 4.1 Thermodynamic T-Matrix in QGP i=Q,q,g j=Q,q,g • Scattering equation • Perturbative approximation (weak coupling): Tij Vij • Strong coupling → resummation: Tij = Vij + ∫ Vij Di Dj Tij • Thermal parton propagators: Di = 1 / [w – wk –Si(w,k)] • Parton self-energies → self-consistency: • q ~ T << mQ q(4)2 = q02 - q2 -q2  3D reduction of Bethe-Salpeter equation • In-medium potential V? j=q,g Si = ij

  16. 4.2 Potential Extraction from Lattice Data • Free Energy - • QQSpectral Function Bayesian Approach T-Matrix Approach V r [fm] • Potential close to free energy • small imaginary parts • Include large imaginary parts • Remnant of confining force! [Burnier et al ’14] [S.Liu+RR ’15, ‘17]

  17. 4.3 Quarkonium Spectral Functions + Correlators Charmonium Bottomonium [S.Liu+RR ‘17] • J/y / ϒ(1S/2S) melting (300/500/250MeV) not inconsistent with pheno.

  18. 4.4 Hamiltonian Approach to QGP • In-Medium Hamiltonian with ``bare” 2-body interactions - effective in-medium mass • Interaction ansatz: Cornell potential with relativistic corrections - color-Coulomb and string (“confining”) interaction - decent spectroscopy in vacuum • Implement into Brueckner / Luttinger-Ward-Baym approach [Liu+RR ‘16]

  19. 4.5 QGP Equation of State + Spectral Functions Thermodynamic Potential Selfconsistent SFs G=G0+G0SG S=GT T=V+VGGT T=194MeV T=400MeV Quark spectral functions  [GeV] “Meson” T-matrix [S.Liu+RR ’16] • Near Tclight partons melt + broad hadronic resonances emerge

  20. 4.6 Transport Coefficients Viscosity and Heavy-Quark Diffusion • Strongly coupled: (2pT) Ds ~ (4p) h/s • Perturbative: (2pT) Ds~ 5/2 (4p) h/s • Transition as T increases

  21. 4.5.2 Sensitivity to Heavy-Quark Transport • Strongly-coupled potential gives max. low-pTc-quark v2 • Weakly-coupled potential (~ free energy) ruled out

  22. 5.) Summary • Quarkonia probe in-medium QCD force, survive into the QGP Regenerated J/y’s vs. suppressed ϒ’s in heavy-ion collisions • Open heavy flavor a more direct probe of in-medium force strength  clear preference of strongly coupled potential (low-pTv2!) • Large scattering rates imply melting of light quasiparticles • Quantum many-body theory to connect heavy-flavor to bulk medium properties to realize premise of Q’s as QGP probe strongly coupled solution toward Tpc predicts (i) melting light partons (ii) hadron formation (iii) small Ds, h/s, …

  23. 4.4.1 Selfconsistent Equation of State for QGP Thermodynamic Potential Skeleton Diagrams n,n • Fully resummed Luttinger-Ward functional (!) • Fit quark+ gluon “bare” masses • Broad hadronic resonances emerge near Tpc [S.Liu+RR ’16]

  24. 2.2 In-Medium ϒ Suppression 1S 2S 1P 1S 2S 1P • Binding energies control reaction rates • ϒ(1S) suppression sensitive to EB(T) • significant regeneration for ϒ(2S)

  25. 3.8 Versatility of Equilibrium Benchmarks • Quarkonium equilibrium abundance in “chemical” transport • Heavy-quark equilibration controls quarkonium regeneration • Heavy-quark transport to satisfy detailed balance (2↔2, 2↔3) • Quark coalescence (energy conservation): equilibrated quarks → equilibrated hadrons (!) • Constraints from lattice QCD

  26. 2.1 Quarkonium Transport in URHICs 0 0.5 5 10 | | | | t [fm/c] fireball time c - c production + evolution of cc wave pack. c-quark diffusion in QGP ~ Tmelt: y can form QGP kinetics c+c↔y ~ Tpc: c and c hadronize - hadronic kinetics - - tform~1fm/c tceq ~5fm/ctyeq~ 1/Gy [Satz et al, Capella et al, Spieles et al, PBM et al, Thews et al, Grandchamp et al, Ko et al, Zhuang et al, Zhao et al, Chaudhuri, Gossiaux et al, Young et al, Ferreiro et al, Strickland et al, Brambilla et al, …]

  27. 3.5 y(2S) in dAu and pPb d-Au (0.2TeV) p-Pb (5.02TeV) [ALICE] [PHENIX] - -EPS09 • noticeable y and little J/ysuppression, consistent with “comovers” • supports fireball formation with: tFBG(y) ~ 1  Gavg(y) ~ 50-100 MeV similar to thermal tFBG(J/y) << 1  Gavg(J/y) < 20 MeV widths at T 200MeV [Ferreiro ‘15] [Du et al ‘15]

  28. 2.3 Quarkonium Width Comparisons Charmonium Bottomonium J/y (1S) melted • Fair agreement for J/y • Larger spread for  states • Binding energies differ (2S) melted

  29. 3.3 Properties of Charmonium Excess • excess concentrated at low pT • low-pT excess carries sizable v2 • systematic softening of J/y pT-spectra with increasing √s → nature of source changes [Tsinghua]

  30. 4.1 Charm Thermalization + J/y Regeneration → Softening of charm-quark spectra facilitates regeneration J/yEquilibrium Fraction Charm-Quark Diffusion Coeff. (Nyeq)off-c / (Nyeq)thermal-c 1-exp[-t /tceq] t /tceq T /Tc [Ko et al ‘12] [Prino+RR ‘16] • Charmonium phenomenology • favors tceq≤ 5 fm/c • (“strong”coupling) Ds = tceq T/mQ≤ (4-8) /(2pT)

  31. 4.3 (1S): Rapidity Puzzle • problem of large(r) suppression in 2.76 TeV ALICE data • beware of cold nuclear matter effects • Regeneration: Nbb ~ 1 for central PbPb canonical limit NY~ (Nbb)1 y

  32. 4.2 (1S) and (2S) Transport cont’d … as implemented in current transport approaches (1S) [Tsinghua] [Ko et al] • (2S) more sensitive sensitive to in-medium potential

  33. 4.5 In-Medium Quarkonium Binding Energies

  34. 2.4 Heavy-Quark Potential + Regeneration Lattice-based potentials [TAMU ‘11,’17] [Kent St ‘17] • (1S)suppression at RHIC→ regeneration at LHC • Regeneration dominant for(2S) in central PbPb at LHC?

  35. 3.3 Heavy-Quark Interactions in QGP Minimal / Desirable Ingredients and Features • Microscopic description of scattering amplitude • Realistic in-medium interaction kernel (screening) • Nonperturbative interactions (color-Coulomb / pQCD not enough) • Resummation (strong coupling) • Hadronization approaching Tc from above (bound states) • Elastic + radiative processes (low / high pT) • Realistic medium partons: quasiparticles, widths, parton spectral functions, …? Equation of state? • Quantitatively rooted in constraints from lattice QCD QGP Q [Caron-Huot+Moore ’08]

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