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Quarkonia in Medium and in Heavy-Ion Collisions

Quarkonia in Medium and in Heavy-Ion Collisions. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA Heavy-Flavor Workshop RHIC & AGS Annual Users Meeting BNL, 21.06.05. link to Lattice QCD. 1.Introduction: The Virtue of HQ’s in URHICs.

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Quarkonia in Medium and in Heavy-Ion Collisions

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  1. Quarkonia in Mediumand in Heavy-Ion Collisions Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA Heavy-Flavor Workshop RHIC & AGS Annual Users Meeting BNL, 21.06.05

  2. link to Lattice QCD 1.Introduction:The Virtue of HQ’s in URHICs • Common lore: , dominantly • produced in primordial NN-collisions • quarkonia: (Ny)prim ≈ x Ncc(x≈1%) •  suppression probes re-interaction • Ncc large  regeneration relevant: • (Ny )second ~ (Ncc )2 [PHENIX ’04] • Consequences of Regeneration: • - charmonium number sensitive to open-charm properties • ►masses: mc, mD vs. my (thermal weights) • ► momentum distribution (y formation) • - Resonances in QGP?! • quarkonia: dissociation/regeneration above Tc • D-mesons: enhanced c-quark rescattering

  3. Outline 1. Introduction 2. c- and b-Quark Interactions in Medium 2.1 Collective Flow, Coalescence 2.2 Rescattering in QGP 3. Quarkonium in Medium 3.1 Basic Elements and Connections to URHICs 3.2 Lattice QCD and Spectral Properties 3.3 Binding, Reaction Rates and Equilibrium Limit 3.4 Kinetic Rate Equation 4. Phenomenology in URHICs 4.1 J/Suppression vs. Regeneration 4.2 Intermediate-Size Ions (A≈100) 4.3 Bottomonium 5. Conclusions

  4. D B PHENIX 130AGeV e± 2.1.1. Open-Charm and e±pt-Spectra - Schematic PYTHIA vs. Thermal+Flow D-Meson Coalescence at Tc [Greco,Ko+RR ’04] [Batsouli,Gyulassy, Kelly+Nagle ’02] PHENIX 200AGeV • very similar on log-scale • 3-mom. mostly in c-quark • note:RAA ≈ 0.2-0.5 for “thermalization”

  5. 2.1.2. Single-e± Elliptic Flow - Schematic jet- quench [Djordjevic etal ’04] Challenges: • dynamical origin of strong re-interactions • cc production • open-bottom “contamination” • onset of pQCD regime (pt > 5-6GeV ?) • consistency v2 ↔ RAA _ [Müller etal ’95, Molnar’04] • Coalescence predictions • based on same c-quark v2 • as for light quarks • jet quenching low?

  6. [van Hees+ RR ’04] • relatively large number of D-states • (8 per u,d, 4 for s) • isotropic cross section 2.2 Resonant Open-Charm Rescattering _ _ “Light”-Quark Resonances c + q → “D” → c + q • effective model with pseudo/scalar • + axial/vector “D-mesons” 1.4Tc [Asakawa+ Hatsuda ’03] • parameters: mD(0), GD

  7. Coordinate Space Diffusion • ‹x2› - ‹x›2 = Dx t ≈ (4-5 fm)2 • ~ fireball size at Tc c-Quark Drag and Diffusion Coefficients in QGP [van Hees+RR ’04] Thermalization Times pQCD “D” • resonance scatt. isotropic • secondary open-charm ?! • [50% for ]

  8. 2.3 Bottom vs. Charm Thermalization in QGP [van Hees+RR ’04] Thermalization Times • charm quark equilibration time ~ fireball lifetime • bottom quarks do not thermalize (RHIC)

  9. - → ← J/y + g c + c + X key ingredients: reaction rate equilibrium limit (y -width) (links to lattice QCD) 3.) Quarkonia in Medium3.1 Basic Elements and Connections to URHICs • 3-Stage Dissociation:nuclear (pre-eq) -- QGP -- HG • Stot = exp[-snucrL] exp[-GQGPtQGP ] exp[-GHGtHG ] • Regeneration in QGP + HG: • - statistical coalescence at Tc: chem.+therm. equil. • - more microscopically: backward reaction (detailed balance!) [PBM etal ’01, Gorenstein etal ’02, …] [Thews etal ’01, Ko etal ’02, Grandchamp+RR ’02, Cassing etal ‘03] for thermal c-quarks and gluons:

  10. 3.2 Lattice QCD + Spectral Properties of Charmonium • Lattice: hc, J/y survive up to ~2Tc • mass my ≈ const • potential screened  binding reduced • eB ~ 2mc* - my mc* decreases with T • Relation to spectral function, ImDy : [Asakawa+ Hatsuda ’03] • real part (pole ) ↔ screening • imaginary part (width) ↔ dissociation: [Datta etal ’03] • microscopic origin?

  11. 3.3.1 Quarkonium Binding Energies in QGP e.g. screened Cornell potential (linear+confining) [Karsch,Mehr+Satz ’88, Wong ’04, …] Charmonium Bottomonium ~Tc ~Tc m~ gT [GeV] m~ gT [GeV] • quarkonium binding energies substantially reduced above Tc

  12. _ Dissociation Times 3.3.2 Charmonium Reaction Rates in QGP • (i)Gluo- • Dissociation • sdiss(w)peaked atw ≈1.4eB • ok for free J/y (eBvac=640MeV) • not in QGP (screened), y’, cc • (ii) “Quasifree” • Dissociation • appropriate for small binding • also involves (anti-) quarks • neglects bound-state structure [Bhanot+Peskin ‘84] [Grandchamp+RR ‘01] Cross Sections

  13. 3.3.3 Bottomonium Reaction Rates in QGP • screening accelerates dissociation substantially • significance at RHIC: tY ≈50 →5 fm/c [Grandchamp,Lumpkins,Sun,van Hees+RR ’05]

  14. - - p,r + J/y → DD,D*D, … Reduced DD threshold (e.g. DmD(Tc )=Dmq≈ -140MeV):   J/y robust (factor ~5 above QGP)  Y’ fragile: direct Y’→ DD decays 3.3.4 Charm(onium) below Tc Hadronic dissociation: Cross Sections Dissociation Times QCD-SR Mes-Ex CQM pQCD

  15. 3.3.5 Charmonium Width+Mass from Lattice QCD [Umeda+ Matsufuru ’05] using constrained curve fitting (Breit-Wigner functions) hcand J/y Mass hcand J/y Width • ”jumps” across Tc • qualitatively consistent with • partonic dissociation • essentially constant

  16. 3.3.6 J/y Equilibrium Abundances smaller mD smaller gc  smaller (Ny) eq [Grandchamp, Brown+RR ’04] • match open-charm states continuously through Tc • correct equil. no. for thermal relaxation: R(t)= 1 - exp[-∫ dt /tceq(T)]

  17. Upsilon • Suppression only! • importance of screening 3.4 Time Evolution of Quarkonia at RHIC Solve kinetic rate-equation: J/y in Central Au-Au • Equilibration close to Tc ?!

  18. J/yExcitation Function • QGP regeneration dominant • sensitive to: • mc* , (Ncc )2 ↔ rapidity, √s, A SPSRHIC 4.) Charmonium in A-A [Grandchamp +RR ’03]

  19. 4.1.2 J/y pt-Spectra in Au-Au at RHIC Quark Coalescence at Tc [Thews+Mangano ’05] [Greco,Ko+RR ’04] • total yields different by factor 3 • large sensitivity to radial flow (bt,max=0.5-0.65)

  20. 4.1.3 Scrutinizing Charmonium Regeneration II: J/y Elliptic Flow Suppression only Thermal Coalescence at Tc [Greco etal ’04] [Wang+Yuan ’02] MB Au-Au • factor ~5 different! • transition inpt!?

  21. NA60 4.2 Intermediate-Mass Ions SPSRHIC [Grandchamp+RR ’04] • onset of regeneration • suppression prevalent

  22. 4.3 Upsilon at RHIC and LHC RHIC LHC [Grandchamp,Lumpokins,Sun,van Hees+RR ’05] • bottomonium suppression as unique QGP signature ?!

  23. Quarkonia in Medium: • - spectral function: include both screening (real part) • and dissociation (imaginary part) • - gluo-dissociation vs. “quasifree” (↔ lattice QCD) • - deconfinement order parameter? width ?! • Quarkonia in URHICs: • - regeneration ~↔ formation in QGP • - evaluate quantitative consequences of • - excitation fct., pt- and v2-spectra, bottomonium suppression?! 5.) Conclusions • Heavy Quarks in Medium: • - essential prerequisite to understand quarkonia in URIHCs • - c-quarks “thermalize”?! (resonances?), b-quarks not …

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