Heavy Quarkonium Transport in Medium - PowerPoint Presentation

1. Heavy Quarkonium Transport in Medium Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, TX, USA rapp@comp.tamu.eduPhysics Opportunities with Quarkonia at the EICCFNS (Stony Brook), OnlineOct. 25-27, 2021

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

3. 1.2 Quarkonia in MediumIn-medium spectral functions: - Mass / binding energy EB(p,T) - Inelastic reaction rate G(p,T;EB)(1S): color-Coulomb force J/y, (2S), …: confining forceConnection to open heavy-flavor transportQGPQQ- Spectral Functionvacuum1-J/y

4. 1.) Introduction2.) Quarkonia at Finite Temperature ● Transport Coefficients ● In-Medium Potential Approach + Lattice QCD ● Binding Energies + Dissociation Rates3.) Phenomenology in Heavy-Ion Collisions ● Excitation Functions + Momentum Dependence ● Lower Collision Energies + Small Systems4.) ConclusionsOutline

5. 2.1 Quarkonium Transport in Heavy-Ion CollisionsJ/yDD-J/yc-c[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, Strickland et al ‘11 …] Semi-classical Transport Boltzmann eq. pm ∂mfy = -Ep Gy fy + Ep b → Rate eq. Transport coefficients - Equilibrium limit: Nyeq(my,T; Ncc) = gc2 ny(T) VFB depends quadratically on charm cross section scc ~ Ncc ~ gc nc VFB y + g,q c + c + X← →-q q gluo-dissociation (“singlet-to-octet”) • “quasi-free”/ Landau damping “Large” binding EB ≥ T“Small” binding EB < mD- Reaction rate Gy (EB(T)): 

6. 2.2 Many-Body Theory of Heavy Flavor in QGPOpen HFobservablesQuarkoniumobservablesQuarkoniumbinding EBQuarkoniumreaction rate GY,equil. limit NYeqMicroscopic Transport in Test in Theory HI collisions Experiment Lat-QCD HQfree energyHQ interactionsin QGP (Ds)Heavy-quarkpotential

7. T-matrix equation2.3 Thermodynamic T-Matrix Approach QQ Free energy:In-medium potential?[TAMU ’05-’18]Vr [fm] Large imaginary parts SI  V > F Remnants of confining force above Tc!  infer in-medium potentialT=258 T=320 T=400 Spectral function:

8. 2.4 More lQCD Constraints: Euclidean Correlators (1S) survives until T > 400 MeV J/y “melts” near T ~ 250-300 MeV Charmonium Bottomonium [Aarts et al ’18][Liu et al ’18]

9. 2.5 Binding Energies + Reaction Rates: Y States1S1S1P2S1P2S1S1P2SReduced binding “accelerates” dissociation (opens phase space)Dissociation rate depends on “medium” particle distribution[Du et al ’18]

10. 2.6 Quarkonium Formation TimesRelatively small effect in heavy-ion collisionsMicroscopically: quantum evolution of wave package Pair production time tQQ ≤ 0.1 fm/c Bound-state formation time tform ~ 1/EB ~ 0.2 - 2 fm/c Build-up of wave function reduces dissociation rate

11. 1.) Introduction2.) Quarkonia at Finite Temperature ● Transport Coefficients ● In-Medium Potential Approach + Lattice QCD ● Binding Energies + Dissociation Rates3.) Phenomenology in Heavy-Ion Collisions ● Excitation Functions + Momentum Dependence ● Lower Collision Energies + Small Systems4.) ConclusionsOutline

12. 3.1 Snapshot of Quarkonium Transport Results mostly suppression substantial regeneration, concentrated at low pT RHIC LHC: centrality LHC: momentum Bottomonia mostly driven by suppression, regeneration small even at the LHC

13. 3.2 Excitation Functions: SPS - RHIC - LHC Gradual increase of total J/y RAA Regeneration and suppression increase Regeneration concentrated at low pT Charmonium Bottomonium Gradual suppression Regeneration (Nϒeq) small Qualitative difference from J/y Data: NA50, PHENIX, STAR, ALICE, CMS [Rapp+Du’17]

14. 3.4 Charmonia at SPS Energy (s=17 GeV) y dissociation in hadronic matter important in transport models [Sorge et al ‘97, Grandchamp et al ‘03, .…][PBM+ Stachel ‘00] Large contributions from initial “nuclear absorption” at low s requires high-energy N-Y Xsec0 100 200 300 400Npart J/y y(3686)

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

16. 4.) SummaryQuarkonia 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/y’s vs. suppressed ϒ’s in heavy-ion collisions Several methods of transport approaches transferable to EIC with nuclear targets

17. r [fm] 0.25 0.5 0.75 1 1.25 1.51.510.50-0.5-1 (2S)J/, (2S)(1S)2.3 Upshot of Quarkonium PhenomenologyUse 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]240350550

18. 2.4 Heavy-Quark Potential Extraction from ϒ DataAnsatz for in-med. potential Parameterize T-dependence of mD~ aT, 1/RSB ~ mS(T;b,g,d)  determine in-med. binding energies EY(mD,mS)Compute GY [EY]Deploy transport approach to fit (a,b,g,d; K) to ϒ data at RHIC + LHCQGPQQ_also requires HQ-medium couplingperturbative: as ~ 0.3non-perturbative: K  5[Du,Liu+RR ‘19]

19. 3.4 Statistical Extraction of Heavy-Quark Potential c2/dof  1 “Strongly-coupled” solution: remnants of confining force survive well above Tc Not unique …Fit Results In-Medium Potential[Du et al ‘19]

20. 3.5 X(3872) Does X(3872) production in heavy-ion collisions reveal internal structure information?Larger size (molecule vs. tetraquark)  larger yield -- or else? With RAAexp(y(2S)) ~ 0.14, RAA(X) compatible with unity pT > 15GeV might be outside coalescence/regeneration regime

21. 3.5.2 In-Medium X(3872) Production Models Transport Approach: Coalescence Models: partons (fi) projected on hadron wave fct. (W)W=W(s) with hadron radius s  NX ~ s3 Nmol >> Ntetra[H. Zhang et al ’20]Reaction rate larger for weakly bound molecule  molecule freeze-out later than tetraquarkEquilibrium limit drops with T  Nmol < Ntetra[B. Wu et al ’20][Cho et al ’11, Fontoura et al. ‘19, …]

22. 3.6 Bc(6275) Critical “universality test” for transport modelsExpect large yields in AA relative to pp [dNc/dy ~ 30 in PbPb(5TeV)] Need to control pp production cross section (denominator): Predictions appear to agree with data… caveats: pp cross section, pT range (theory: pT > 0, data: pT3m > 6 GeV)RAA (pT) ≡ (dN/dpT)AA / Ncoll (dN/dpT)pp Theory Prediction [Wu et al. ‘21] CMS Data

23. | | | | 2.1 Quarkonium Transport in URHICsct [fm/c]0 0.5 5 10[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, …] c-fireball time production + evolution of cc wave pack.~ Tpc:c and c hadronizehadronic kinetics ~ Tmelt: y can formtform~1fm/c tceq ~5fm/c tyeq ~ 1/ Gy QGPkineticsc+c ↔ y-c-quark diffusion in QGP--