Theoretical Perspective on Quarkonia from SPS via RHIC

Theoretical Perspective on Quarkonia from SPS via RHIC to LHC Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, TX USA XXVI Int. Conference on Ultra-Relativistic Heavy-Ion Collisions Quark Matter 2017 Chicago (IL, USA), Feb. 05 -11, 2017

1. ) Introduction: A “Calibrated” QCD Force 1. 5 1 [Ge. V] V 1 [Ge. V] 0. 5 T=0 0 -0. 5 r [fm] -1 0. 25 0. 75 1 1. 25 1. 5 • Vacuum quarkonium spectroscopy well described • Confinement ↔ linear part of potential [Bazavov et al ‘ 13] Opportunity: Utilize quarkonia to probe in-medium QCD force ↔ infer consequences for transport coeffs. + spectral functs. ↔ probe QGP properties at varying resolution

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) • Model constraints from lattice QCD • (1 S): color-Coulomb J/ , (2 S), …: confining force • How do heavy quarks within quarkonia interact with the medium? • Not a good thermometer… [Rothkopf]

1. 3 Quarkonium Transport in URHICs 0 | 0. 5 | fireball time t [fm/c] c 5 | 10 | c- production + c-quark evolution of diffusion cc- wave pack. in QGP tform~1 fm/c tceq ~5 fm/c ~ Tmelt: can form QGP kinetics c+c- ↔ t eq ~ 1/ G ~ Tpc: hadronic c and c kinetics hadronize [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, …]

Outline 1. ) Introduction 2. ) Theoretical Tools 3. ) Quarkonium Excitation Functions 4. ) Force-Strength Probes 5. ) Conclusions

2. ) Theoretical Tools • Statistical Hadronization model: chem. equil. of charm hadrons � • Transport Approaches Boltzmann equat. � → Rate equation • Reaction Rate G “Strong” binding EB ≥ T • gluo-dissosciation (“singlet-to-octet”) [Bhanot+Peskin ’ 85, Brambilla et al ’ 08, Liu et al ‘ 13…] “Weak” binding EB < m. D q q • “quasi-free”/ Landau damping [Grandchamp+RR ‘ 02, Song et al ’ 07, Laine et al‘ 07, …]

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

Outline 1. ) Introduction 2. ) Theoretical Tools 3. ) Quarkonium Excitation Functions 4. ) Force-Strength Probes 5. ) Conclusions

3. 1 Excitation Functions in Au. Au and Pb. Pb Charmonium mid-rap Bottomonium • | | MB mid-rap • | | • Gradual increase of total J/ RAA • Regeneration and suppression increase • Cold- vs. Hot-nuclear-matter effects… [data: NA 50, PHENIX, STAR, ALICE, CMS] • Gradual suppression • (2 S) melts at RHIC, (1 S) melts at LHC • Role of regeneration?

3. 2 Attempt to Divide out Cold-Nucl. -Matter Effects RAAhot RAAtot / SCNM • J/ suppressed at SPS mostly from feeddown ( N ~7. 5 mb), melts in the RHIC → LHC regime (not unlike (2 S))

3. 3 Properties of Charmonium Excess • excess concentrated at low p. T • low-p. T excess carries sizable v 2 • systematic softening of J/ p. T -spectra with increasing √s → nature of source changes [Tsinghua]

3. 4 Upshot of Quarkonium Phenomenology Use temperature estimtates from hydro/photons/dileptons to infer: T 0 SPS (~240) < Tmelt(J/ , ) ≤ T 0 RHIC (~350) < Tmelt( ) ≤ T 0 LHC (~550) • • Remnants of confining force survive at SPS Confining force screened at RHIC+LHC Color-Coulomb screening at LHC Thermalizing charm quarks recombine at LHC 1. 5 1 550 350 240 (2 S) J/ , (2 S) (1 S) 0. 5 0 cf. [Petreczky] -0. 5 r [fm] -1 0. 25 0. 5 [hold J/ together] [“melts” J/ + (2 S)] [ (1 S) suppression] [large J/ yield] 0. 75 1 1. 25 1. 5

3. 5 (2 S) in d. Au and p. Pb d-Au (0. 2 Te. V) [PHENIX] p-Pb (5. 02 Te. V) [ALICE] - - EPS 09 • noticeable and little J/ suppression, consistent with “comovers” • supports fireball formation with: t. FB G( ) ~ 1 Gavg( ) ~ 50 -100 Me. V t. FB G(J/ ) << 1 Gavg(J/ ) < 20 Me. V [Ferreiro ‘ 15] similar to thermal widths at T 200 Me. V [Du et al ‘ 15]

Outline 1. ) Introduction 2. ) Theoretical Tools 3. ) Quarkonium Excitation Functions 4. ) Force-Strength Probes 5. ) Conclusions

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

4. 2 Heavy-Quark Potential and (1 S) Suppression Input “Potential” UQQ [Kent St] [TAMU] FQQ • (1 S) suppression prefers “strong” (U) over “weak” (F) in-med. potential • role of regeneration for (1 S), (2 S) ?

5. ) Summary • Transport analyses of quarkonia in URHICs suggest interplay of dissociation+formation processes of diffusing Q’s with “strong” potential • Different states probe T-dependence of binding + reaction rates; remnant of confining force in QGP → strongly coupled medium!? • Charmonia RAA(Npart) also consistent with statistical hadronization at Tc • Further progress - exp. : heavy-quark cross section, (2 S) and cc, b states (feeddown), (3 S) at RHIC, rapidity “puzzle”, (1 S, 2 S) v 2 (regeneration) - theo. : scrutinize assumptions + inputs, quantum evol. of QQ wave packg. , tighten constraints from l. QCD on HQ pot. + transport coeffs. , … Many thanks for help in preparing: Xiaojian Du, Baoyi Chen, Yunpeng Liu, A. Andronic, E. Ferreiro, M. Strickland, P. Zhuang

4. 3 (1 S): Rapidity Puzzle • problem of large(r) suppression in 2. 76 Te. V ALICE data • beware of cold nuclear matter effects • Regeneration: Nbb ~ 1 for central Pb. Pb canonical limit NY ~ (Nbb)1 y

4. 2 (1 S) and (2 S) Transport cont’d … as implemented in current transport approaches (1 S) [Tsinghua] [Ko et al] • (2 S) more sensitive to in-medium potential

4. 5 In-Medium Quarkonium Binding Energies

4. 5 pt Spectra in Pb-Pb(5. 02 Te. V)

4. 4 Regeneration and Elliptic Flow • Sizeable effect only for (2 S)

2. 1 Potential Extraction from Lattice Data • Free Energy • QQ Spectral Function Bayesian Approach T-Matrix Approach U V F lattice data 1. 2 Tc r [fm] • Potential close to free energy [Burnier et al ’ 14] • Account for large imaginary parts • Remnant of confining force! [S. Liu+RR ’ 15]

3. 3 Heavy-Flavor Transport at RHIC + LHC • flow bump in RAA + large v 2 ↔ strong coupling near Tpc (recombination) • high-precision v 2: transition from elastic to radiative regime?