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: c c and b b dominantly produced in primary NN-collisions ⇒ heavy simultaneously probe: - jet quenching - coalescence - thermalization

- u,d,s chemistry (e.g. Ds enhancement) • In-Medium Modifications: - D- masses; D=(cq): thresholds, χiral Restoration?! - Resonances in QGP?!

Quarkonia: dissociation/regeneration above Tc D-: 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/ψ 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: c f ٭ j f STAR ٭ i c dσ dσ → D = f (x ) f (x ) ij cc ∫ i 1 j 2 ˆ DD/c(z) dxF dt Factorization + π- - + 0 0 ± 0 Fragmentation N D /D D /D D /D (isospin symmetry + D*/D=3) Frag 1 1 1/3 Exp 1.35±0.05 0.93±0.03 0.415±0.01

marked flavor asymmetries not accounted for ! 2.2 Recombination Approach

• historically: forward π+/π- , K+/K- asymmetries [Das+Hwa ’77, … ] [Likhoded etal ’80s, Hwa ’95, • similarly for c-quarks: recomb. with qval Braaten etal ’02, …]

• here: recomb. also with sea-quarks; [RR+Shuryak ‘03] > Input: π q i D ▪ 2-parton distribution fct.: >c (2) = − − p fiq C2 fq (xq ) fi (x1) (1 xq x1) ▪ recombination fct.: N σ σ = ∆ 2 2 πσ2 R(yq , yc, y) exp( y /2 y)/ 2 y

rec 2 d dx dz ⎛d σ ⎞ x* (cq) = q ⎜ c,q ⎟ R (x ,z;x ) dx ∫∫x z ⎜ dx dz ⎟ (cq) q F F q ⎝ q ⎠ Recombination + Fragmentation Approach [RR+Shuryak ’03]

− = recombination substantial D cd − even at central xF π = du

Do = cu

flavor-asym. reproduced ok 3. c-Quark Interactions in HI Collisions [Dokshitzer+Kharzeev’01, • high pt : pQCD E-loss ↔ modified frag. Djordjevic etal ’03, …]

• intermediate pσt : (onset of) coalescence [Lin+Molnar ’03, µ Greco,Ko+RR ’03,…] d p dND = π µ 3 ψ r 2 r r E gD d q | D(q)| fq(pq) fc(pc) d3p ∫∫(2 )3 π fq : thermal light quarks incl. v0 , v2 from fit to , K fc : c-quark distribution, e.g.: - PYTHIA ↔ no reinteractions - thermal incl. v , v (also: c + c → Ψ ) 0 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+FlowElliptic FlowD-Meson Coalescence at Tc

[STAR D Prelim]

B

PHENIX PHENIX 130AGeV e± 200AGeV

[PHENIX Prelim] practically indistinguishable not very sensitive either [Batsouli,Gyulassy,Kelly+Nagle ’02] [Greco,Ko+RR ’03] ψ J/ pt-Spectra: Coalescence at Tc

• total yields different by factor 3 β • large sensitivity to radial flow ( t,max=0.5-0.65) 4.) Charm(onium) in the QGP 4.1 Heavy-Quark Thermalization?!

2 2 2 2 • Naively: 1 scatt. Q ≈ T , (pt,therm) ≈ mcT ⇒ Nscatt≈(pt,therm/Q) ≈5 • more quantitative: Boltzmann Eq. [Svetitsky ’88] ∂ ⎡∂f ⎤ f ( p,t ) = = d 3k [ w( p + k ,k ) f ( p + k )− w( p,k ) f ( p ) ] ∂ ⎢ ∂ ⎥ ∫ t ⎣ t ⎦coll ∂f ∂( pf ) ∂2 f ⇒ = γ + D 1-D Fokker Planck Eq. ∂t ∂p ∂p2 1 −[ p− p (t)]2 / 2σ 2 −E /T γp = d 3k w(k, p) k scatt. rate f ( p,t) = e 0 → e p ∫ 2πσ 2 σ = 1 3 D − γ D d k w(k, p) k diff. const. (t)2 = (1− e 2 t ) 2 ∫ γ α • e.g.: pQCD Xsections (gc→gc), T=500MeV, s=0.6(0.3) ⇒ γ = 0.25 (0.06) fm-1 ↔ τ = 4-15fm/c (very) slow! Resonant Open-Charm Rescattering _ _ c + q → “D” → c + q “Light”-Quark Resonances • effective model with pseudo/scalar + axial/vector “D-mesons” 1.4Tc + / [Asakawa+ = (1 v ) Γ φ + LDcq GD q D c h.c. Hatsuda ’03] 2 µ Γ = γ γ γ γ 1, 5 , , 5 µ

• chirally symmetric for light quarks • heavy-quark symmetry µ ⇒ j conserved to LO(1/mc) (0) • parameters: mD , GD [van Hees+RR ’04] c-Quark Drag and Diffusion Constants in QGP [van Hees+RR ’04] Thermalization Times Coordinate Space Diffusion

• resonance scatt. isotropic 2 2 2 • ‹x ›-‹x› = Dx t ≈ (4-5 fm) • secondary open-charm ?! ~ fireball size at Tc [50% for 3 × σ ( gg → c c ) ] 4.2 Charmonium in QGP η ψ • Lattice:ψ c, J/ survive up to ~2Tc τψ * •mass mψ ≈ const ~ 2mc •width: 3π Γ = −1 = d k q,g σ diss f (T ) q,g−ψ vrel ∫ (2 )3 [Datta etal ’03]

gluo-dissociation, inefficient for * mψ≈ 2 mc

“quasifree” dissoc. [Grandchamp+RR ’01] 4.3 Time Evolution and Regeneration • statistical coalescence at T : thermal equilib. [Braun-Munzinger etal ’01, c Gorenstein etal ’02, …] • charmonia above Tc ⇒ formation in QGP: detailed balance! [Thews etal ’01, Ko etal ’02, Grandchamp+RR ’02, …] J/ψ + g → c + c- + X ψ ← for thermalized c-quarks: ψ dN ψ eq τ = − Γ ( N − Nψ ) d * Au-Au “jumps” at Tc ? sensitive to Ncc , mc √s=200GeV rather direct link to lattice QCD!

Equilibration close to Tc ?! 5.) Charmonium in A-A SPS RHIC [Grandchamp +RR ’03] J/ψ Excitation Function

• QGP regeneration dominant • sensitive to:

mc* , open-charm degeneracy, 2 (Ncc) ↔ rapidity, √s, A 5.2 Lighter Ions SPS RHIC

In-In √s=18AGeV

[Grandchamp+RR ’04] • suppression • onset of regeneration 6. Conclusions • Elementary collisions: - “soft” recomb.: chemistry pre-established by PDF’s? - baseline for heavy ions • URHICs:

Open Charm: E-loss / coalescence (pt), equilibration (v2) ↔ resonances?!

Charmonium: - regeneration if v2(D) large Γ * - formation in QGP ↔ ψ (T) , mc (T) τ -(Ncc,V, QGP) ↔ (Npart,y,√s) - deconfinement order parameter? Bottomonium Suppression at RHIC ?! Additional Slides 4. Charmed Mesons in Medium ψ 4.1 Hadronic : D-Mesonsτψ and ψ’ π ρ 3 − d k m (T,ρ ) expected to decrease Γ = 1 = π f , σπdissρ v D B ∫ 3 , −ψ rel (Chiral Symmetry Restoration) (2 )

[Weise etal ’01]

⇒ reduced threshold for • ψ [Grandchamp+RR ’03] π,ρ + Ψ J/ robust → DD • Ψ’ fragile: Ψ’→ DD decays 5.3 Open-Charm Chemistry

Central A-A p-p (Statistical Model) (Frag. + Recomb.) [Andronic et al. ’03] [RR+Shuryak ’03] √s [GeV] 17 200 17 200 D± / D0 0.456 0.454 0.39 0.4 D- / D+ 1.6 1.04 1.35 1.24 D0 / D0 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 η=0Æ2: CGC [Tuchin], Color-Dipole [Raufeisen]

•LHC: CGC: Npart ; nonlin. DGLAP: enhanced! [Kolhinen]

(ii) pT-Spectra ± v2(e ) : Thermalization?! dE/dx : Null Effect?! [Djordjevic] [PHENIX] preliminary

[PHENIX] preliminary 3.4 Hydro vs. Coalescence: The 2-6GeV Regime [Hirano,Nara] [Fries,Hwa,Molnar]σ µ d πp dNh = µ 3 ψ r 2 r r E gh d q | h (q) | f a( pa ) fb ( pb ) d 3 p ∫∫(2 )3

[PHENIX] [STAR] [Greco etal.]

v2: mass-dependent ⇒ universal partonic v2(pT/n) / n But: p/π(4GeV)≈0.3 soft-soft ≈ thermal ( pT »m) [PHENIX]: 1±0.15 soft-hard: explicit thermal+jet (correlations!) Challenges: p/π=1 + jet correlation , φ elliptic flow ψ τψ π ρ 2.3 Charm(onium) below Tc 3π − d k Γ = 1 = f , (E T)σπdissρ ()s v Dissociation rate ∫ 3 k, , −ψ rel −− (2 ) π + J/ψ → DD,D*D [Grandchamp+RR ’03] QCD-SR Mes-Ex

CQM pQCD

∆ Reduced DD threshold: mD(Tc)≈-140MeV (NJL) ⇒ • J/ψ robust • Ψ’ fragile: direct Ψ’→ DD decays