Quarkonia in Medium and their Fate at Future RHIC Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA Workshop on “Future Perspectives in QCD at High Energy” Brookhaven National Laboratory,

1.) Introduction: Quarkonia Probing the QGP immerse -pair into the QGP  Vacuum properties change: color screening (reduced binding) dissociation reactions (and reverse!) heavy-quark mass (→ mass and decay rates, threshold) Experiment: no direct access (?) to spectral shape (unlike  → e + e - ): J/  decay outside medium with 1:200 (  : 5:1) number of J/ ,  ’, Y, … and their p T -spectra, v 2 (p T ) Challenges: - in-Medium -spectral functions - infer confinement of QGP! order parameter?!

1.) Introduction 2.) Medium Effects on Quarkonia 2.1 Color Screening 2.2 Dissociation Reactions 2.3 Heavy-Quark Masses in QGP 2.4 Spectral Functions and Correlators ↔ Lattice QCD 3.) Phenomenology in URHICs 3.1 Suppression and Regeneration 3.2 The Role of Open Charm 3.3 Observables 4.) Summary and Outlook Outline

2.1 Onia in QGP: Color Screening and Binding [Shuryak etal ’04, Wong ’04, Alberico etal ’05, Mocsy etal ‘05, …] small binding energies above T c (~ screened Cornell pot.) even smaller(!) for V 1 = (1-  U 1 +  F 1 solve Schrödinger-Eq. with lattice-QCD U 1 (r) as potential Bottomonium Charmonium [Wong ’06]

(i) Gluo- Dissociation  diss (  ) peaked at  ≈1.4  B ok for free J/  B vac =640MeV  not for screening,  ’,  c Charmonia in QGP: Dissociation Reactions [Bhanot+Peskin ‘84] Cross Sections (ii) “Quasifree” Dissociation neglects bound-state structure appropriate for small binding also involves (anti-) quarks [Grandchamp+RR ‘01] _ Dissociation Times

2.2.2 Bottomonium Lifetimes in QGP [Grandchamp etal ’05] appreciable sensitivity to color screening! significance at RHIC:  Y ≈ 50 → 5 fm/c  ~ gT [GeV] ~T c [Karsch,Mehr +Satz ‘88] “Quasifree” Suppression Bottomonium Screening

2.3 Heavy-Quark Masses in the QGP [Kaczmarek +Zantow ‘05] in-/decreasing heavy-quark mass ?! close to T c : entropy contribution? quarkonium mass: m  = 2m c * -  B asymptotic energies F ∞ = U ∞ - TS ∞ U∞U∞ F∞F∞

2.4 Spectral Functions and Euclidean Correlators Vacuum Spectral Function ~ Bound State + Continuum:   (  ) = F  2  (   -m  ) +  2   -  thr  f  thr In-Medium Bound-State / Resonance   (  ) ~ Im D   : - real part (pole ) ↔ screening, in-medium quark-mass - imaginary part (width) ↔ dissociation e.g.   = ‹ n p  diss v rel › ≈ 10 fm -3 1mb ½ ≈ 100 MeV (T≈250MeV) for  QGP =2fm/c: S  = exp[-     QGP ] ≈ 0.37  “stable” J/  at RHIC unlikely  2  J/  ’’ cont. In-Medium Continuum: E thr (T), nonperturbative Q-Q rescattering _

2.4.2 Euclidean Correlation Functions (or R = G / G recon ) accurate “data” from lattice QCD, integral over spectral function S-wave charmonia little changed to ~2T c, P-wave signal enhanced(!) cc cc [Datta etal ‘04]

2.4.3 Euclidean Correlator -- Potential Model Spectral Function:   (  = F  2  (   - m  ) +  2   -  thr  f  thr - Bound State: Schrödinger eq. with screened Cornell, or lQCD U 1 - Continuum: pQCD with E thr (T) = 2m c +V ∞ opposite trend as on lattice compatible with lattice increase due to reduced E thr (T)! [Mocsy+Petreczky ‘05]

2.4.4 Eucl. Correlator -- Model II: T-Matrix Approach use potential to solve Lippmann-Schwinger-Eq. for Q-Q T-Matrix: - [Mannarelli+RR ’05, Cabrera+RR in prep] Correlator: [Cabrera+RR in prep] comprehensive treatment of bound and scattering states nonperturbative threshold effects large finite-width effects

2.4.4 Eucl. Correlators from T-Matrix Approach lattice U 1 -potential, m c =1.7GeV fix, G recon (E thr =2m D ) [Cabrera+RR in prep] cc cc trends roughly as on lattice, except magn. + T-dep. of  c ; threshold?! [Datta etal ’04]

2.4.4 Eucl. Correlators from T-Matrix Approach lattice U 1 -potential, m c =1.7GeV fix, G recon = G(T=1.1T c ) [Cabrera+RR in prep] sensitive to G recon ! ~ insensitive to width effects! cc

3.) Phenomenology in URHICs 3.1 Suppression + Regeneration 3.2 The Role of Open Charm 3.3 Observables

3-Stage Dissociation: nuclear (pre-eq) -- QGP -- HG S tot = exp[-  nuc   L] exp[-  QGP  QGP ] exp[-  HG   HG ] Regeneration in QGP + HG: - microscopically: backward reaction (detailed balance!) key ingredients: reaction rate equilibrium limit (  -width) (links to lattice QCD) 3.1 Suppression and Regeneration in URHICs [PBM etal ’01, Gorenstein etal ’02,Thews etal ’01, Grandchamp+RR ’01, Ko etal ’02, Cassing etal ‘03] J/  + g c + c + X ← → - - for thermal c-quarks and gluons:  -  nuc (SPS) ≈ 4.5mb → used for RHIC predictions; - but: RHIC d-Au data →  nuc ≈1.5mb

softer c-quarks → more  formation ↔ c-quark diffusion:  c eq = m c T/D 3.2 The Role of Open Charm and Regeneration [van Hees etal ‘05] e ± Spectra need more detailed studies! (e.g. transport, Langevin) [Greco etal ‘05] pQCD scatt. nonpert. scatt. yields differ by factor 3 importance of Cronin [Thews+ Mangano’05] [Ko etal ’02, Cassing etal ‘03 Gossiaux etal ’06, Zhang ’06, …] J/  Coalescence at T c

 nuc =4.4mb,  c eq ~ 2.5fm/c (schem.) QGP-regeneration dominant sensitive to: m c *, (N cc ) Observables I: Centrality Dependence at RHIC [Grandchamp etal ’03] → solve rate equation for expanding fireball (QGP-mix-hadron gas) Original Predictions [PHENIX ‘05]  nuc =1.5mb sensitive to: c-quark diff., T diss shape of R AA a problem?! precise data! [X.Zhao+RR in prep] Update and Further Studies

nontrivial “flat” dependence similar interplay in rapidity!? (need accurate dN c /dy) Observables II: Excitation Function + Rapidity J/  Suppression vs. Regeneration [Grandchamp +RR ’01] direct J/  essentially survive (even at RHIC) Sequential  ’+  c Suppression [Karsch,Kharzeev+Satz ‘06]

RHIC [Grandchamp etal ’05] Bottomonium at RHIC and LHC 50% feeddown from Y’,  b importance of color-screening! bottomonium suppression as unique QGP signature ?! LHC

5.) Summary strong color-screening from lQCD heavy-quark potentials short quarkonium lifetimes (  X =1-5 fm/c) open-charm masses: open problem Heavy-Ion Collisions: - J/  above T c : gain term! sensitive to c-quark diffusion, T diss - flat excitation fct.: suppr. vs regeneration or (  ’,  c ) only? elliptic flow: v 2 (J/  ) up to ~10% ?! - Y suppression (very) sensitive to screening - sQGP signature: Y more suppressed than J/  at RHIC+LHC ! Euclidean Correlation Functions: - quantitative constraints on model spectral functions - importance of nonperturbative threshold effects (T-matrix!) - moderate sensitivity to width effects

2.4.4 Eucl. Correlators from T-Matrix Approach lattice U 1 -potential, m c =1.8GeV fix, G recon (E thr =2m D ) [Cabrera+RR in prep] trends roughly agree with lattice, except T-dep. of  c – threshold?! cc cc

QGP-suppression prevalent “jumps” / ”plateaus” in centrality? 3.5 Charmonium Observables at SPS Pb(158AGeV)-Pb In(158AGeV) –In [Grandchamp etal ’03] Satz, Digal, Fortunato Rapp, Grandchamp, Brown Capella, Ferreiro Percolation Plasma Comovers NA60 preliminary

2.1 Onia in QGP: Color Screening and Binding Energies [Karsch,Mehr+Satz ’88, Wong ’04, …] binding energies much reduced above T c similar for lattice U 1 (r), smaller(!) for F 1 e.g. screened Cornell potential (linear+confining) Charmonium Bottomonium ~T c  ~ gT [GeV] ~T c

2.4.1 Langevin-Simul. at RHIC: Heavy-Quark R AA [van Hees,Greco+RR ’05] Resonances vs. pQCD Charm-pQCD (  s,  D =1.5T)  s, g 1, , ,1.8 [Moore and Teaney ’04] hydro with T c =165MeV,  ≈ 9fm/c  s and Debye mass independent expanding fireball ≈ hydro pQCD elastic scatt. moderate resonance effects substantial

3.4.3 Scrutinizing Charmonium Regeneration II: J/  Elliptic Flow Suppression only Thermal Coalescence at T c [Wang+Yuan ’02] [Greco etal ’04] MB Au-Au factor ~5 different! transition in p t !?