InMedium Quarkonia at RHIC and LHC Ralf Rapp

In-Medium Quarkonia at RHIC and LHC Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, TX USA Workshop on “Newest Quarkonia Results” RHIC & AGS Annual Users’ Meeting BNL (Upton, NY), 17. -20. 06. 14

1. ) Introduction: A “Calibrated” QCD Force V [½ Ge. V] r [½ fm] [Kaczmarek et al ‘ 03] • Vacuum charm-/bottomonium spectroscopy well described • Confinement? ! Operational criterion: linear part of potential • most sensitive to J/y + ’ (EBCoul(J/y) ~ 0. 05 Ge. V vs. 0. 6 Ge. V exp. ) • nonperturbative treatment • potential approach in medium?

Outline 1. ) Introduction 2. ) Quarkonium Transport in Medium 3. ) Comparison to RHIC + LHC Data 4. ) Conclusions

2. ) Quarkonium Transport in Heavy-Ion Collisions • Inelastic Reactions: [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, …] → c + c- + X detailed balance: J/y + g ← • Rate Equation: D - D J/y c- c J/y • Theoretical Input: Transport coefficients - chemical relaxation rate Gy - equililbrium limit Nyeq(ey. B, mc* , tceq) • Phenomenological Input: - J/y, cc, y’+c, b initial distributions [pp, p. A] - space-time medium evolution [AA: hydro, . . . ] Observables

2. 1 Thermal Charmonium Properties (a) Equilibrium Y number: • gc from fixed cc- number: • interplay of mc* and • constrain spectral shape by lattice-QCD correlators (b) Inelastic Y Width e y. B mc * q q • controlled by as (parameter) Gy

2. 2 Effect of Partial c-Quark Thermalization on J/y • Relaxation time ansatz: Nyeq (t) ~ Nytherm(t) · [1 -exp(-t/tceq)] Microscopic Calculation Impact on Regeneration [Zhao+RR ‘ 11] [Song, Han, Ko ‘ 12] • sensitivity of regeneration on charm-quark diffusion

3. 1 Inclusive J/y at SPS + RHIC Strong Binding (U) Weak Binding (F) [Zhao+RR ‘ 10] • as~0. 3, charm relax. tceq = 4(2) fm/c for U(F) vs. ~5(10) from T-matrix • different composition in two scenarios

3. 1. 2 J/y p. T Spectra + Elliptic Flow at RHIC (strong binding) • shallow minimum at low p. T • high p. T: formation time, b feeddown, Cronin • small v 2 limits regeneration, but does not exclude it

3. 1. 3 J/y Excitation Function: BES at RHIC PHENIX (forward y) STAR (central y) • suppression pattern varies little (expected from transport) [Grandchamp +RR ’ 02] • quantitative pp + p. A baseline critical to extract systematics

3. 2. 1 J/y Predictions at LHC [Zhao+RR ‘ 11] • regeneration becomes dominant • uncertainties in scc+shadowing • low p. T maximum confirms regeneration

3. 2. 2 J/y at LHC: v 2 [He et al ’ 12] • further increase at mid-y

3. 3 (1 S) and (2 S) at LHC Weak Binding Strong Binding (1 S) → (2 S) → [Grandchamp et al ’ 06, Emerick et al ‘ 11] • sensitive to color-screening + early evolution times • clear preference for strong binding (U potential) • similar results by [Strickland ‘ 12]

4. ) Conclusions • Quarkonium discoveries in URHICs: - increase of J/y RAA SPS, RHIC → LHC - low-p. T enhancement - sizable v 2 - increasing suppression of ’ (e. B ’ ~ e. BJ/y ) • Predicted signatures of QGP transport + hadronization - controlled by quantitative description of RHIC+SPS data, lattice QCD • Implications - T 0 SPS (~230) < Tdiss(J/y, ’) < T 0 RHIC (~350) < T 0 LHC(~550) ≤ Tdiss( ) - confining force screened at RHIC+LHC - marked recombination of diffusing charm quarks at LHC • Uncertainties - input HF cross sections, HF thermalization - initial-state effects (final-state in d. Au, p. Pb? !)

2. ) Thermodynamic T-Matrix in QGP • Lippmann-Schwinger equation In-Medium - T-Matrix: Q-Q • potential Va real - propagator G ) • imaginary parts: unitarization (cuts in in-med. QQ QQ • simultaneous treatment of: - bound + scattering states - quarkonia (QQ) + heavy-quark diffusion (Qq, g) [Wong, Mannarelli+RR, Mocsy+Petreczky, Beraudo et al. , Song et al. , Riek+RR, …]

2. 2 Brueckner Theory of Heavy Quarks in QGP Input Process Q→Q 0 -modes 2 -body potential Quark selfenergy - QQ T-matrix Qq T-matrix Output Test quark-no. susceptibility spectral fcts. / eucl. correlat. lattice data - evolution QQ (rate equation) exp. data Q spectra + v 2 (Langevin)

2. ) Thermodynamic T-Matrix for Quarkonia in QGP • Lippmann-Schwinger equation In-Medium Q-Q T-Matrix: • potential Va strictly real • imaginary parts: unitarization (cuts in in-med. QQ propagator GQQ) q • gluo-dissosciation (coupled channel) [Bhanot+Peskin ‘ 85] q • Landau damping (HQ selfenergy)

2. 3 Free vs. Internal Energy in Lattice QCD F 1(r, T) = U 1(r, T) – T Free Energy. S 1(r, T) Internal Energy - potential • weak QQ • small m. Q* ~ m. Q + F 1(∞, T)/2 [Kaczmarek +Zantow ’ 05] • strong QQ potential, U = ‹H int› • large m. Q* ~ m. Q + U 1(∞, T)/2 • F, U, S thermodynamic quantities • Entropy: many-body effects

3. 2. 2 D-Meson Thermalization at LHC • to be determined…

3. 3. 3 J/y at LHC III: High-pt – ATLAS+CMS [Zhao+RR ‘ 11] • underestimate for peripheral (spherical fireball reduces surface effects …)

3. 3. 4 Time Evolution of J/y at LHC Strong Binding (U) Weak Binding (F) • finite “cooking-time” window, determined by inelastic width [Zhao+RR ‘ 11]

3. 4 at RHIC and LHC Weak Binding Strong Binding RHIC → LHC → [Grandchamp et al ’ 06, Emerick et al ‘ 11] • sensitive to color-screening + early evolution times

3. 2 Charmonia in QGP: T-Matrix Approach • U-potential, selfconsist. c-quark width • Spectral Functions - J/y melting at ~1. 5 Tc - cc melting at ~Tc - Gc ~ 100 Me. V • Correlator Ratios - rough agreement with l. QCD within uncertainties [Mocsy+ Petreczky ’ 05+’ 08, Wong ’ 06, Cabrera+RR ’ 06, Beraudo et al ’ 06, Satz et al ’ 08, Lee et al ’ 09, Riek+RR ’ 10, …] [Aarts et al ‘ 07]

3. 2. 2 T-matrix Approach with F-Potential • selfcons. c-quark width • Spectral Functions - J/y melting at ~1. 1 Tc - cc melting at ≤ Tc - Gc ~ 50 Me. V • Correlator Ratios - slightly worse agreement with l. QCD [Riek+RR ’ 10] [Aarts et al ‘ 07]

3. 3 Charm-Quark Susceptibility in QGP → G→ 0 2 → m «T [Riek+RR ‘ 10] • sensitive to in-medium charm-quark mass • finite-width effects can compensate in-medium mass increase

gc [1/fm] 4. 2. 5. 2 Thermalization Rate from T-Matrix • thermalization 4 (2) times faster using U (F) as potential than pert. QCD • momentum dependence essential (nonpert. effect ≠ K-factor!) [Riek+RR ‘ 10]

3. 1. 3 Momentum Dependence of Inelastic Width • dashed lines: gluo-dissociation • solid lines: quasifree dissociation _ • similar to full NLO calculation [Zhao+RR ‘ 07] [Park et al ‘ 07]

4. 3 J/y at Forward Rapidity at RHIC [Zhao+ RR ‘ 10]