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From Heavy-Flavor Transport to Bulk and Spectral Properties of the QGP
11/28/2018 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 Frankfurt University (Germany) June 14, 2018
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1.) Heavy Quarks: A “Calibrated” QCD Force
[GeV] V [½ GeV] 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
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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…
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1.3 Heavy Quarks in Medium Q Diffusion: “Brownian motion”
Thermalization delayed by mQ/T → memory in URHICs Direct access to transport coefficient Ds (2πT) (~ η/s ~ sEM/T !?) Scattering rates → widths (quantum effects); quasiparticles? (mQT) → simple estimate: Ds(2pT)=3 GQ ~1GeV - Implications for QGP structure? Non-perturbative effects Probe of hadronization (Ds, Lc) Q QGP Q
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Outline 1.) Introduction 2.) Quarkonia ● Transport Coefficients
11/28/2018 Outline 1.) Introduction 2.) Quarkonia ● Transport Coefficients ● Phenomenology 3.) Open Heavy Flavor ● Brownian Motion of Heavy Quarks 4.) Many-Body Theory of Heavy Quarks + QGP ● T-Matrix Approach ● QGP Properties 5.) Conclusions
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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 D - c J/y + g c + c + X ← Rate equation: Transport coefficients - Equilibrium limit Nyeq(my,T; Ncc) q q gluo-dissosciation (“singlet-to-octet”) • “quasi-free”/ Landau damping “Strong” binding EB ≥ T “Weak” binding EB < mD - Reaction Rate Gy (EB(T))
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2.2 Excitation Functions: SPS - RHIC - LHC
Charmonium Bottomonium Gradual increase of total J/y RAA 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
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2.3 Upshot of Quarkonium Phenomenology
11/28/2018 Use temperature estimates from hydro/photons/dileptons to 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 at RHIC+LHC [“melts” J/y + (2S)] Color-Coulomb screening at LHC [(1S) suppression] Thermalizing charm quarks recombine at LHC [large J/y yield] r [fm] 1.5 1 0.5 -0.5 -1 (2S) J/, (2S) (1S) 240 350 550
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Outline 1.) Introduction 2.) Quarkonia ● Transport Coefficients
11/28/2018 Outline 1.) Introduction 2.) Quarkonia ● Transport Coefficients ● Phenomenology 3.) Open Heavy Flavor ● Brownian Motion of Heavy Quarks 4.) Many-Body Theory of Heavy Quarks + QGP ● T-Matrix Approach ● QGP Properties 5.) Conclusions
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3.1 Heavy-Flavor Transport in URHICs
| | | | 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 Tpc and 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, …]
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3.2 Heavy-Flavor Transport
p2 ~ mQ T >> q2 ~ T2 Brownian Motion: Fokker- Planck Q thermalization rate diffusion coefficient g p = d3q wQ(q,p) q ~ |TQj|2 (1-cosq) f j Dp = d3q wQ(q,p) q2 thermal relaxation time tQ = 1/g Einstein relation: T = Dp / g mQ spatial diffusion constant: Ds = T / g mQ , <x2> - <x>2 = 6 Ds t relation to bulk medium: Ds (2pT) ~ h / s (4π)
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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
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3.4 Spatial Charm-Quark Diffusion Coefficient
Ds = T / (mQ gQ(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
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Outline 1.) Introduction 2.) Quarkonia ● Transport Coefficients
11/28/2018 Outline 1.) Introduction 2.) Quarkonia ● Transport Coefficients ● Phenomenology 3.) Open Heavy Flavor ● Brownian Motion of Heavy Quarks 4.) Many-Body Theory of Heavy Quarks + QGP ● T-Matrix Approach ● QGP Properties 5.) Conclusions
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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
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4.2 Potential Extraction from Lattice Data
Free Energy - QQ Spectral 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]
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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.
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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]
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4.5 QGP Equation of State + Spectral Functions
Thermodynamic Potential Selfconsistent SFs G=G0+G0S G S=GT T=V+VGGT T=194MeV T=400MeV Quark spectral functions [GeV] “Meson” T-matrix [S.Liu+RR ’16] Near Tc light partons melt + broad hadronic resonances emerge
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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
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4.5.2 Sensitivity to Heavy-Quark Transport
Strongly-coupled potential gives max. low-pT c-quark v2 Weakly-coupled potential (~ free energy) ruled out
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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-pT v2!) 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, …
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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]
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2.2 In-Medium ϒ Suppression
11/28/2018 2.2 In-Medium ϒ Suppression 1P 2S 1S 1S 1P 2S Binding energies control reaction rates ϒ(1S) suppression sensitive to EB(T) significant regeneration for ϒ(2S)
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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
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2.1 Quarkonium Transport in URHICs
| | | | fireball time t [fm/c] c - c production + evolution of cc wave pack. ~ Tpc: c and c hadronize hadronic kinetics ~ Tmelt: y can form tform~1fm/c tceq ~5fm/c tyeq ~ 1/ Gy QGP c+c ↔ y - c-quark diffusion in QGP [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, …]
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3.5 y(2S) in dAu and pPb d-Au (0.2TeV) p-Pb (5.02TeV)
[ALICE] [PHENIX] - - EPS09 noticeable y and little J/y suppression, consistent with “comovers” supports fireball formation with: tFB G(y) ~ 1 Gavg(y) ~ MeV similar to thermal tFB G(J/y) << 1 Gavg(J/y) < 20 MeV widths at T 200MeV [Ferreiro ‘15] [Du et al ‘15]
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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
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3.3 Properties of Charmonium Excess
• systematic softening of J/y pT -spectra with increasing √s → nature of source changes [Tsinghua] excess concentrated at low pT • low-pT excess carries sizable v2
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4.1 Charm Thermalization + J/y Regeneration
→ Softening of charm-quark spectra facilitates regeneration J/y Equilibrium 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)
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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
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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
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4.5 In-Medium Quarkonium Binding Energies
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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?
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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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