Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision

1. Thermal Kinetic Equation Approach to Charmonium Production in Heavy-Ion Collision Xingbo Zhao with Ralf Rapp Department of Physics and Astronomy Iowa State University Ames, USA Brookhaven National Lab, Upton, NY, Jun. 14th 2011

2. Outline • Thermal rate-equation approach • Dissociation rate in quasi-free approximation • Regeneration rate from detailed balance • Connection with lattice QCD • Numerical results compared to exp. data • Collision energy dependence (SPS->RHIC->LHC) • Transverse momentum dependence (RHIC) • Rapidity dependence (RHIC)

3. Motivation: Probe for Deconfinement • Charmonium (Ψ): a probe for deconfinement • Color-Debye screening reduces binding energy -> Ψ dissolve • Reduced yield expected in AA collisions relative to superposition of individual NN collisions • Other factors may also suppress Ψ yield in AA collision • Quantitative calculation is needed [Matsui and Satz. ‘86]

4. Motivation: Eq. Properties Heavy-Ion Coll. • Equilibrium properties obtained from lattice QCD • free energy between two static quarks ( heavy quark potential) • Ψ current-current correlator ( spectral function) • Kinetic approach needed to translate staticΨ eq. properties into production in the dynamically evolving hot and dense medium ? ?

5. D - J/ψ D c - c J/ψ Picture of Ψ production in Heavy-Ion Coll. • 3 stages: 1->2->3 • Initial production in hard collisions • Pre-equilibrium stage (CNM effects) • Thermalized medium • 2 processes in thermal medium: • Dissociation by screening & collision • Regeneration from coalescence • Fireball life is too short for equilibration • Kinetic approach needed for off-equilibrium system

6. Thermal Rate-Equation • Thermal rate-equation is employed to describe production in thermal medium (stage 3) • Loss termfor dissociation Gain term for regeneration • Γ: dissociation rate Nψeq: eq. limit of Ψ • Detailed balance is satisfied by sharing common Γ in the loss and gain term • Main microscopic inputs: Γ and Nψeq

7. Link between Lattice QCD and Exp. Data Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator

8. Link between Lattice QCD and Exp. Data Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator

9. In-medium Dissociation Mechanisms • Dissociation rate: • Dissociation cross section σiΨ • gluo-dissociation: VS. quasifreedissociation: g+Ψ→c+ g(q)+Ψ→c+ +g(q) [Bhanot and Peskin ‘79] [Grandchamp and Rapp ‘01] • Gluo-dissociation is not applicable for reduced εBΨ<T • quasifree diss. becomes dominant suppression mechanism • strong coupling αs~ 0.3 is a parameter of the approach

10. Link between Lattice QCD and Exp. Data Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator

11. Charmonium In-Medium Binding • Potential model employed to evaluate [Cabrera et al. ’07,Rieket al. ‘10] [Petreczky et al ‘10] • V(r)=U(r) vs. F(r)? (F=U-TS) • 2 “extreme” cases: • V=U: strong binding • V=F: weak binding [Riek et al. ‘10]

12. T and p Dependence of Quasifree Rate • Gluo-dissociation is inefficient even in the strong binding scenario (V=U) • Quasifree rate increases with both temperature and ψ momentum • Dependence on both is more pronounced in the strong binding scenario

13. Link between Lattice QCD and Exp. Data Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator

14. Link between Lattice QCD and Exp. Data Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator

15. Model Spectral Functions • Model spectral function = resonance + continuum • In vacuum: • At finite temperature: quasifree diss. rate • Z(T) reflects medium induced change of resonance strength • Z(T) is constrained from matching lQCDcorrelator ratio pole mass mΨ threshold 2mc* Tdiss=2.0Tc V=U Tdiss=1.25Tc V=F widthΓΨ Tdiss Z(Tdiss)=0 • Regeneration is possible • only if T<Tdiss Tdiss

16. Correlators and Spectral Functions weak binding strong binding [Petreczky et al. ‘07] • Peak structure in spectral function dissolves at Tdiss • Model correlator ratios are compatible with lQCDresults

17. Link between Lattice QCD and Exp. Data Initial conditions Kinetic equations Experimental observables diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator

18. Regeneration: Inverse Dissociation • Gain term dictated by detailed balance: • • For thermal c spectra, NΨeqfollows from statistical model • charm quarks distributed over open charm and Ψ states according to their mass and degeneracy • masses for open charm and Ψ are from potential model [Braun-Munzinger et al. ’00, Gorenstein et al. ‘01] • Realistic off-kinetic-eq. c spectra lead to weakerregeneration: • Charm relaxation time τceq is our second parameter: τceq~3/6fm/c

19. Link between Lattice QCD and Exp. Data Initial conditions Kinetic equations Experimental observables shadowing nuclear absorption Cronin diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator

20. Link between Lattice QCD and Exp. Data Initial conditions Kinetic equations Experimental observables Coll. energy dep. Pt dep. Rapidity dep. shadowing nuclear absorption Cronin diss. & reg. rate: Γ Ψ eq. limit: NΨeq εBΨ mΨ, mc lQCD potential lQCDcorrelator

21. Compare to data from SPS NA50 weak binding (V=F) strong binding(V=U) incl. J/psi yield • Different composition for different scenarios • Primordial production dominates in strong binding scenario • Significant regeneration in weak binding scenario • Large uncertainty on σcc

22. J/Ψ yield at RHIC incl. J/psi yield weak binding (V=F) strong binding(V=U) • Larger primordial (regeneration) component in V=U (V=F) • Compared to SPS regeneration takes larger fraction in both scenarios • Formation time effect and B meson feeddown are included See also [Thews ‘05],[Yan et al. ‘06],[Andronic et al. ‘07]

23. J/Ψ yield at LHC (w/o Shadowing) weak binding (V=F) strong binding(V=U) • Parameter free prediction – both αs and τceq fixed at SPS and RHIC • Regeneration component dominates except for peripheral collisions • RAA<1 for central collisions (with , ) • Comparable total yield for V=F and V=U

24. With Shadowing Included • Shadowing suppresses both primordial production and regeneration • Regeneration dominant in central collisions even with shadowing • Nearly flat centrality dep. due to interplay between prim. and reg.

25. Compare to Statistical Model weak binding (V=F) strong binding(V=U) • Regeneration is lower than statistical limit: • statistical limit in QGP phase is more relevant for ψ regeneration • statistical limit in QGP is smaller than in hadronic phase • charm quark kinetic off-eq. reduces ψ regeneration • J/ψ is chemically off-equilibrium with cc (small reaction rate)

26. High ptΨ at LHC • Negligible regeneration for pt > 6.5 GeV • Strong suppression for prompt J/Ψ • Significant yield from B feeddown • Similar yields and composition between V=U and V=F

27. Pt Dependence at RHIC Mid-Rapidity V=U V=U see also [Y.Liu et al. ‘09] • Primordial production dominant at pt>5GeV • Regeneration concentrated at low pt due to c quark thermalization • Formation time effect and B feeddown increase high pt production [Gavin and Vogt ‘90, Blaizot and Ollitrault ‘88, Karsch and Petronzio ‘88]

28. RAA(pT) at RHIC Mid-Rapidity V=F V=F • At low pt regeneration component is larger than V=U

29. J/ψ v2(pT) at RHIC strong binding(V=U) weak binding(V=F) • Small v2(pT) for entire pT range • At low pt v2 from thermal coalescence is small • At high ptregeneration component is gone • Even smaller v2 even in V=F • Small v2 does not exclude coalescence component

30. J/ΨYield at RHIC Forward Rapidity incl. J/psi yield weak binding (V=F) strong binding(V=U) • Hot medium induced suppression and reg. comparable to mid-y • Stronger CNM induced suppression leads to smaller RAA than mid-y • Larger uncertainty on CNM effects at forward-y See also [Thews ‘05],[Yan et al. ‘06],[Andronic et al. ‘07]

31. RAA(pT) at RHIC Forward Rapidity V=U V=U • Shadowing pronounced at low pt & fade away at high pt • Large uncertainty on CNM effects

32. RAA(pT) at RHIC Forward Rapidity V=F V=F • At low pt reg. component is larger than V=U (similar to mid-y)

33. Summary and Outlook A thermal rate-equation approach is employed to describe charmonium production in heavy-ion collisions Dissociation and regeneration rates are compatible with lattice QCD results J/ψ inclusive yield consistent with experimental data from collision energy over more than two orders of magnitude Primordial production (regenration) dominant at SPS (LHC) RAA<1 at LHC (despite dominance of regeneration) due to incomplete thermalization (unless the charm cross section is really large) • Calculate Ψ regeneration from realistic time-dependent charm • phase space distribution from e.g., Langevin simulations 33

34. Thank you! based on X. Zhao and R. Rapp Phys. Lett. B 664, 253 (2008) X. Zhao and R. Rapp Phys. Rev. C 82, 064905 (2010) X. Zhao and R. Rapp Nucl. Phys. A 859, 114 (2011)

35. Compare to data from SPS NA50 weak binding (V=F) strong binding(V=U) incl. J/psi yield trans. momentum • primordial production dominates in strong binding scenario

36. J/ψ v2(pT) at RHIC strong binding(V=U) • Small v2(pT) for entire pT range

37. Explicit Calculation of Regeneration Rate • in previous treatment, regeneration rate was evaluated using detailed balance • was evaluated using statistical model assuming thermal charm quark distribution • thermal charm quark distribution is not realistic even at RHIC ( ) • need to calculate regeneration rate explicitly from non-thermal charm distribution [van Hees et al. ’08,Riek et al. ‘10]

38. 3-to-2 to 2-to-2 Reduction diss. • g(q)+Ψc+c+g(q) reg. dissociation: regeneration: • reduction of transition matrix according to detailed balance

39. Thermal vs. pQCD Charm Spectra • regeneration from two types of charm spectra are evaluated: 1) thermal spectra: 2) pQCD spectra: [van Hees ‘05]

40. Reg. Rates from Different c Spectra See also, [Greco et al. ’03, Yan et al ‘06] • thermal : pQCD : pQCD+thermal = 1 : 0.28 : 0.47 • strongest reg. from thermal spectra (larger phase space overlap) • introducing c andangular correlation decrease reg. for high ptΨ

41. ΨRegeneration from Different c Spectra • strongestregeneration from thermal charm spectra • pQCD spectra lead to larger <pt2> of regenerated Ψ • c angular correlation lead to small reg. and low <pt2> • blastwaveoverestimates <pt2> from thermal charm spectra

42. V=F V=U larger fraction for reg.Ψ in weak binding scenario strongbinding tends to reproduce <pt2> data J/Ψ yield and <pt2> at RHIC forward y incl. J/psi yield trans. momentum 42

43. J/Ψ suppression at forward vs mid-y comparable hot medium effects stronger suppression at forward rapidity due to CNM effects 43

44. RAA(pT) at RHIC V=F V=U • Primordial component dominates at high pt (>5GeV) • Significant regeneration component at low pt • Formation time effect and B-feeddown enhance high pt J/Ψ • See also [Gavin and Vogt ‘90, Blaizot and Ollitrault ‘88, Karsch and Petronzio ‘88] [Y.Liu et al. ‘09]

45. J/Ψ Abundance vs. Time at RHIC V=F V=U • Dissoc. and Reg. mostly occur at QGP and mix phase • “Dip” structure for the weak binding scenario 45

46. J/Ψ Abundance vs. Time at LHC V=F V=U • regeneration is below statistical equilibrium limit 46

47. Ψ Reg. in Canonical Ensemble • Integer charm pair produced in each event • c and anti-c simultaneously produced in each event, • c and anti-c correlation volume • effect further increases • local c (anti-c) density

48. Ψ Reg. in Canonical Ensemble • Larger regeneration in canonical ensemble • Canonical ensemble effect is more pronounced for non-central collisions • Correlation volume effect further increases Ψ regeneration

49. Fireball Evolution , {vz,at,az} “consistent” with: - final light-hadron flow - hydro-dynamical evolution isentropicalexpansion with constantStot(matched to Nch) and s/nB(inferred from hadro-chemistry) EoS: ideal massive parton gas in QGP, resonance gas in HG [X.Zhao+R.Rapp ‘08] 49

50. Primordial and Regeneration Components • Linearity of Boltzmann Eq. allows for decomposition of primordial and regeneration components • For primordial component we directly solve homogeneous Boltzmann Eq. • For regeneration component we solve a Rate Eq. for inclusive yield and estimate its pt spectra using a locally thermal distribution boosted by medium flow.