Quarkonium in Medium and Transport in Heavy-Ion Collisions
Discussing the properties and behavior of quarkonium in medium and its transport in heavy-ion collisions. Topics include heavy-quark potential, confinement, quarkonia at finite temperature, quarkonium transport, and quarkonia in heavy-ion collisions. Insightful details about in-medium potential and binding energies, spectral functions, and gradual loss of binding energies are presented.
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Quarkonium in Medium and Transport in Heavy-Ion Collisions Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station (TX, USA) The 10th International Conference on Quarks and Nuclear Physics, Barcelona (Spain), July 08-12, 2024
Intro-1: Heavy-Quark Potential + Confinement Quarks glued together by strings (2S) (3S) (2S) J/ (1S) V(r) [0.5 GeV] Fs(r) = const 1 GeV/fm 105 N Cornell Potential: V(r) = - 4/3 s/r + r [Kaczmarek et al 05] - Describes heavy-quark bound-state spectra (charmonium + bottomonium) - Confirmed by numerical simulations (lattice QCD) - Manifestation of confinement r [0.5 fm] a well-calibrated force!
Intro-2: Quarkonia in Medium In-medium properties: - Mass / binding energy EB(p,T) - Inelastic reaction rate (p,T;EB) [GeV] (1S): color-Coulomb force J/ , (2S), : confining force [Bazavov et al 13] Screening lowers binding energies EB(T) opens phase space for dissociation Dissociation rate (p;T) is key transport parameter for phenomenology QGP Q Q Connection to open heavy-flavor transport
Outline 1.) Introduction 2.) Quarkonia at Finite Temperature -- In-Medium Potential + Binding Energies 3.) Quarkonium Transport -- Kinetic Approaches + Coefficients 4.) Quarkonia in Heavy-Ion Collisions -- Charmonium + Bottomonium -- Bc(6275) 5.) Summary
2.1 Thermodynamic T-Matrix Approach Q - T-matrix equation In-medium potential? Q Infer V via constraints from lattice QCD (free energy): T=194 MeV T=320 MeV Weak screening, large collisional widths Im Remnants of confining force above Tc! V > F [Liu+RR 15]
2.3 Quarkonium Spectral Functions Bc [Tang et al 23] [Liu et al 18] J/ melts near T~ 300 MeV (cb) states in between and P-waves dissolve much earlier (1S) survives to T ~ 500 MeV
2.4 In-Medium Quarkonium Binding Energies Gradual loss of binding sequential dissolution
Outline 1.) Introduction 2.) Quarkonia at Finite Temperature -- In-Medium Potential + Binding Energies 3.) Quarkonium Transport -- Kinetic Approaches + Coefficients 4.) Quarkonia in Heavy-Ion Collisions -- Charmonium + Bottomonium -- Bc(6275) 5.) Summary
3.1 Quarkonium Transport in URHICs 0 0.5 5 10 | | | | [fm/c] fireball time c c- production + CNM effects cc wave pack. - c-quark diffusion in QGP ~ Tmelt: can form QGP kinetics c+c - ~ Tpc: c and c hadronize hadronic kinetics - form 1fm/c ceq ~5fm/c 1/EB eq ~ 1/ (quantum) (quantum)
3.2 Quarkonium Transport Models in QCD Matter Statistical Hadronization Model Along with all other hadrons, quarkonia are produced at QCD phase boundary [PBM+Stachel 00, Gorenstein et al 02, , Andronic et al 21] Semiclassical Transport Models Evolve quarkonium phase space distributions through QCD medium, initial suppression followed by regeneration for T < Tmelt (even in QGP) et al 03, Zhuang et al 05, Zhao et al 07, Ferreiro et al 11, van Hees et al ] Open Quantum Systems Evolve QQ-reduced density matrix in heat bath (EB << heat) Quantum-Brownian Motion ,n= =Cn Cn [Spieles et al 97, Thews et al 01, Grandchamp+RR 01, Ko et al 02, Bratkovskaya - [Akamatsu, Blaizot et al, Brambilla et al, Escobedo et al, Yao et al, Gossiaux et al, Song et al, ]
3.3 Semiclassical Transport + Coefficients Semi-classical transport Boltzmann eq. p f = Ep f + Ep D - D J/ ?? ?? ??) = (? ? Rate equation: c- c J/ eq(m ,T;Ncc) = c2 n (T) VFB Equilibrium limit: N - Heavy-quark number ~ conserved after initial hard production introduce fugacity c(T): Ncc = c nc(T) VFB(t) cc N eqdepends quadratically on charm cross section!
- + g,q c + c + X Reaction rate in QGP: (p,T,EB) ~ d3pi,f (4)(Pi-Pf)|Mi ccX|2 fi(1-ff) Large binding EB T: gluo-dissociation ( singlet-to-octet ) Small binding EB< mD quasi-free/Landau damping q q Gluo-dissociation small, inelastic scattering dominates
3.4 Binding Energies + Reaction Rates: Y States 1S 1P 2S 1S 2S 1P 1S 1P 2S [Du et al 18] Reduced binding accelerates dissociation (opens phase space) Dissociation rate depends on medium particle distribution
Outline 1.) Introduction 2.) Quarkonia at Finite Temperature -- In-Medium Potential + Binding Energies 3.) Quarkonium Transport -- Kinetic Approaches + Coefficients 4.) Quarkonia in Heavy-Ion Collisions -- Charmonium + Bottomonium -- Bc(6275) 5.) Summary
4.1 Key Observables in Heavy-Ion Collisions Nuclear modification factor: Quarkonium yield in AA relative to pp collisions: ??????? ????? ??????? RAA( (Npart) ) = nnn Peripheral Collision: Central Collision: Npart ~ 350 Npart ~ 40 t [fm/c]
4.2 J/ at SPS (17 GeV) and RHIC (200 GeV) Ti ~ 350 MeV Ti ~ 230 MeV Large nuclear absorption at low s SPS: J/ suppression mostly from excited states feeddown : c , J/ + X RHIC: suppression and regeneration increase!
4.3 Charmonia at the LHC (5020 GeV) Centrality pT Dependence Ti ~ 550 MeV Mid- Rapidity Forward Rapidity Substantial regeneration, concentrated at low pT
4.4 Bottomonium Transport RHIC LHC Ti ~ 550 MeV Ti ~ 350 MeV Strong suppression; similar for (1S) at RHIC + LHC ? Regeneration significant for (2S) at LHC ?
4.5 Excitation Functions: SPS - RHIC - LHC Charmonium Bottomonium Gradual increase of total J/ RAA Regeneration and suppression increase Regeneration concentrated at low pT Gradual suppression Regeneration (N eq) small Qualitative difference from J/ [NA50, PHENIX, STAR, ALICE, CMS]
4.6 Bc(6275) Universality test for transport models Rare in pp collisions (c + b quark needed) dNc/dy ~ 30 in Pb-Pb(5TeV) collisions Need low-pT data! caveat: pp cross section in the denominator [Wu et al 24]
5.) Summary Quarkonia can probe in-medium QCD force (not temperature) Remnants of confining force prevail above Tc quarkonium ground states survive (well) into the QGP (+ key role in generating strongly coupled QGP) Semi-classical transport approaches predict interplay of regenerated J/ s vs. suppressed s in heavy-ion collisions Exotic quarkonia provide further unique insights + tests Ongoing theory efforts to develop + apply quarkonia quantum evolutions, scrutinizing the robustness of semi-classical approaches
3.2 Snapshot of Quarkonium Transport Results RHIC LHC: centrality LHC: momentum mostly suppression substantial regeneration, concentrated at low pT Bottomonia mostly driven by suppression, regeneration small even at the LHC
4.6 X(3872) Does X(3872) production in heavy-ion collisions reveal internal structure information? Larger size (molecule vs. tetraquark) larger yield -- or else?
4.6.2 In-Medium X(3872) Production Models Coalescence Models: parton (fi) projection on hadron wave fct. W( ) : hadron radius NX ~ Nmol >> Ntetra [H. Zhang et al 20] ??? ?? Transport Approach: [B. Wu et al 20] ??) = ? (?? ?? - Equilibrium limit larger for more strongly bound state Nmol < Ntetra
3.4 Charmonia - Open-HF Coupling II: Elliptic Flow QGP charm-quark diffusion + resonance recombination Recombination reaches out to pT ~ 8 GeV[He,Wu+RR 22]
2.4 Heavy-Quark Potential Extraction from Data Ansatz for in-med. potential Parameterize T-dependence of mD~ T, 1/RSB ~ mS(T; ) determine in-med. binding energies EY(mD,mS) Compute Y [EY] - also requires HQ-medium coupling - perturbative: s ~ 0.3 - non-perturbative: K 5 QGP _ Q Q Deploy transport approach to fit ( ; K) to data at RHIC + LHC [Du,Liu+RR 19]
3.4 Statistical Extraction of Heavy-Quark Potential Fit Results In-Medium Potential Strongly-coupled solution: remnants of confining force survive well above Tc Not unique [Du et al 19] 2/dof 1
3.3 Coupling of Quarkonia + Open HF Transport QGP c- Boltzmann: c Gain term: Quasifree: Simultaneous c-quark diffusion + charmonium kinetics (same M2pQCD * K) J/ yield + spectral shape require K 5 Strong coupling for open + hidden HF [Du+RR 22]
3.5 (2S) in dAu and pPb d-Au (0.2TeV) p-Pb (5.02TeV) [ALICE] [PHENIX] - -EPS09 noticeable and little J/ suppression, consistent with comovers [Ferreiro 15] supports fireball formation with: FB ( ) ~ 1 FB (J/ ) << 1 avg( ) ~ 50-100 MeV similar to thermal avg(J/ ) < 20 MeV widths at T 200MeV [Du et al 15]
2.1 Quarkonium Spectroscopy in Vacuum Cornell Potential T-matrix equation Q - Q Tij = Vij+ Vij Gi Gj Tij Relativistic corrections (Breit correction) Spin-spin + spin-orbit interactions Vector component in confining interaction
