Quark Coalescence and Charmonium in QGP Ralf Rapp

Quark Coalescence and Charm(onium) in QGP Ralf Rapp (Texas A&M University) “Hard Probes 2004” Ericeira (Portugal), 06. 11. 04

1. Introduction: The Virtue of HQ’s in URHICs • Common lore: and dominantly produced in primary NN-collisions heavy quarks simultaneously probe: - jet quenching - coalescence - thermalization - u, d, s chemistry (e. g. Ds enhancement) • In-Medium Modifications: - D-meson masses; D=(cq): thresholds, ciral Restoration? ! - Resonances in QGP? ! Quarkonia: dissociation/regeneration above Tc D-mesons: enhanced c-quark rescattering → link to lattice QCD

Outline 1. Introduction 2. Open Charm in Hadronic Collisions Flavor Asymmetries: Fragmentation vs. Recombination 3. c-Quark Interactions in Heavy-Ion Reactions Coalescence, Collective Flow 4. Charm(onium) in QGP 4. 1 Heavy-Quark Thermalization 4. 2 Inelastic Charmonium Reactions 4. 3 Kinetic Rate Equation 5. Phenomenology in URHICs 5. 1 J/ Suppression vs. Regeneration 5. 2 Lighter Ions (A≈100) 6. Conclusions

2. Open-Charm in Hadronic Collisions 2. 1 Production Systematics of D-Mesons Baseline: fj ٭ ٭ fi ٭ STAR DD/c(z) Factorization + Fragmentation (isospin symmetry + D*/D=3) p -N D-/D+ Frag 1 Exp D 0/D 0 1 D±/D 0 1/3 1. 35± 0. 05 0. 93± 0. 03 0. 415± 0. 01 marked flavor asymmetries not accounted for !

2. 2 Recombination Approach [Das+Hwa ’ 77, … ] • historically: forward p+/p- , K+/K- asymmetries [Likhoded etal ’ 80 s, Hwa ’ 95, • similarly for c-quarks: recomb. with qval Braaten etal ’ 02, …] • here: recomb. also with sea-quarks; [RR+Shuryak ‘ 03] Input: D ▪ 2 -parton distribution fct. : p > N > ▪ recombination fct. :

Recombination + Fragmentation Approach [RR+Shuryak ’ 03] recombination substantial even at central x. F flavor-asym. reproduced ok

3. c-Quark Interactions in HI Collisions • high pt : p. QCD E-loss ↔ modified frag. • intermediate pt : (onset of) coalescence [Dokshitzer+Kharzeev’ 01, Djordjevic etal ’ 03, …] [Lin+Molnar ’ 03, Greco, Ko+RR ’ 03, …] fq : thermal light quarks incl. v 0 , v 2 from fit to p , K fc : c-quark distribution, e. g. : - PYTHIA ↔ no reinteractions (also: ) - thermal incl. v 0 , v 2 Limitations: energy conservation (sudden approx. ), mq*, … • low pt : rescattering → thermalization → “statistical coalescence” ? !

Open-Charm and e± pt-Spectra in Au-Au PYTHIA vs. Thermal+Flow D-Meson Coalescence at Tc Elliptic Flow [STAR Prelim] D B PHENIX 130 AGe. V PHENIX 200 AGe. V e± [PHENIX Prelim] practically indistinguishable [Batsouli, Gyulassy, Kelly+Nagle ’ 02] not very sensitive either [Greco, Ko+RR ’ 03]

J/y pt-Spectra: Coalescence at Tc • total yields different by factor 3 • large sensitivity to radial flow (bt, max=0. 5 -0. 65)

4. ) Charm(onium) in the QGP 4. 1 Heavy-Quark Thermalization? ! • Naively: 1 scatt. Q 2≈ T 2, (pt, therm)2≈ mc. T Nscatt≈(pt, therm/Q)2 ≈5 • more quantitative: Boltzmann Eq. [Svetitsky ’ 88] 1 -D Fokker Planck Eq. scatt. rate diff. const. • e. g. : p. QCD Xsections (gc→gc), T=500 Me. V, as=0. 6(0. 3) g = 0. 25 (0. 06) fm-1 ↔ t = 4 -15 fm/c (very) slow!

Resonant Open-Charm Rescattering _ _ c + q → “D” → c + q • effective model with pseudo/scalar + axial/vector “D-mesons” “Light”-Quark Resonances 1. 4 Tc [Asakawa+ Hatsuda ’ 03] • chirally symmetric for light quarks • heavy-quark symmetry jm conserved to LO(1/mc) • parameters: m. D(0), GD [van Hees+RR ’ 04]

c-Quark Drag and Diffusion Constants in QGP [van Hees+RR ’ 04] Thermalization Times • resonance scatt. isotropic • secondary open-charm ? ! [50% for ] Coordinate Space Diffusion • ‹x 2› - ‹x› 2 = Dx t ≈ (4 -5 fm)2 ~ fireball size at Tc

4. 2 Charmonium in QGP • Lattice: hc, J/ survive up to ~2 Tc • mass m ≈ const ~ 2 mc* • width: [Datta etal ’ 03] gluo-dissociation, inefficient for m ≈ 2 m c * “quasifree” dissoc. [Grandchamp+RR ’ 01]

4. 3 Time Evolution and Regeneration etal ’ 01, • statistical coalescence at Tc: thermal equilib. [Braun-Munzinger Gorenstein etal ’ 02, …] • charmonia above Tc formation in QGP: detailed balance! [Thews etal ’ 01, Ko etal ’ 02, J/y + g → c +X ← Grandchamp+RR ’ 02, …] for thermalized c-quarks: “jumps” at Tc ? sensitive to rather direct link to lattice QCD! Equilibration close to Tc ? ! Au-Au √s=200 Ge. V

SPS 5. ) Charmonium in A-A [Grandchamp +RR ’ 03] RHIC J/y Excitation Function • QGP regeneration dominant • sensitive to: mc* , open-charm degeneracy, (Ncc)2 ↔ rapidity, √s, A

5. 2 Lighter Ions SPS RHIC In-In √s=18 AGe. V [Grandchamp+RR ’ 04] • suppression • onset of regeneration

6. Conclusions • Elementary hadron collisions: - “soft” recomb. : chemistry pre-established by PDF’s? - baseline for heavy ions • URHICs: Open Charm: E-loss / coalescence (pt), equilibration (v 2) ↔ resonances? ! Charmonium: - regeneration if v 2(D) large - formation in QGP ↔ - (Ncc, V, t. QGP) ↔ (Npart, y, √s) - deconfinement order parameter? Bottomonium Suppression at RHIC ? !

Additional Slides

4. Charmed Mesons in Medium 4. 1 Hadronic Matter: D-Mesons and ψ’ m. D(T, r. B) expected to decrease (Chiral Symmetry Restoration) [Weise etal ’ 01] reduced threshold for p, r + Y → DD [Grandchamp+RR ’ 03] J/y robust Y’ fragile: Y’→ DD decays

5. 3 Open-Charm Chemistry Central A-A (Statistical Model) [Andronic et al. ’ 03] √s [Ge. V] p-p (Frag. + Recomb. ) [RR+Shuryak ’ 03] 17 200 D± / D 0 0. 456 0. 454 0. 39 0. 4 D- / D + 1. 6 1. 04 1. 35 1. 24 D 0 / D 0 1. 59 1. 05 1. 4 1. 35 Ds / D 0. 253 0. 260 0. 14 0. 23

4. 3 Charm I: Open Charm (Central A-A) (i) Yields • RHIC: -30% for h=0 2: CGC [Tuchin], Color-Dipole [Raufeisen] • LHC: CGC: Npart ; nonlin. DGLAP: enhanced! [Kolhinen] (ii) p. T-Spectra d. E/dx : Null Effect? ! [Djordjevic] [PHENIX] preliminary v 2(e±) : Thermalization? ! [PHENIX] preliminary

3. 4 Hydro vs. Coalescence: The 2 -6 Ge. V Regime [Hirano, Nara] [Fries, Hwa, Molnar] v 2: mass-dependent But: p/p(4 Ge. V)≈0. 3 [PHENIX]: 1± 0. 15 [STAR] [Greco et al. ] [PHENIX] universal partonic v 2(p. T/n) / n soft-soft ≈ thermal ( p. T » m ) soft-hard: explicit thermal+jet (correlations!) Challenges: p/p=1 + jet correlation , f elliptic flow

2. 3 Charm(onium) below Tc Dissociation rate p + J/y → DD, D*D [Grandchamp+RR ’ 03] QCD-SR Mes-Ex CQM p. QCD Reduced DD threshold: Dm. D(Tc)≈-140 Me. V (NJL) J/y robust Y’ fragile: direct Y’→ DD decays