J/ ψ production and elliptic flow in relativistic heavy-ion collisions

1. J/ψ production and elliptic flow in relativistic heavy-ion collisions Taesoo Song (Texas A&M Univ., USA) Reference : T. Song, C. M. Ko, S. H. Lee and J. Xu, arXiv:1008.2730

2. Contents • Introduction • Schematic model forfireball expansion • Thermal properties of charmonia • Charmoniain heavy-ion collisions • Results • Summary

3. 1. introduction

4. QCD phase diagram

5. J/ψ suppression • Long time ago, J/ψ suppression was suggested by Matsui and Satz as a signature of QGP formation in heavy-ion collisions. (due to color screening between c and anti-c) • The suppression was observed at SPS & RHIC. • LQCD suggests the dissociation temperature of J/ψ higher than Tc. • J/ψ is still one of the promising diagnostic probes for hot nuclear matter created by heavy-ion collisions.

6. Phenomenological models 1. Statistical model (P. Braun-Munzinger) Low dissociation temperature of J/ψ Most J/ψ in heavy-on collisions are regenerated ones. 2. Two-component model (R. Rapp) High dissociation temperature of J/ψ Some of J/ψ come from regeneration, some of them come from initial production.

7. NJ/ψ vs. Npartstatistical model two-component model

8. NJ/ψ vs. Ptstatistical model two-component model

9. Questions • How can both models successfully describe experimental data? • How can both models be discriminated?

10. 2. Schematic model for expanding fireball • Initial condition • Equation of state (EoS) • modeling

11. 2. 1. Glauber model b-s s b

12. 2. 2. Initial condition Charged particle multiplicities PRC65, 061901 (2002)

13. EoS of QGP • Quasiparticle picture Noninteracting massive partons to reproduce thermal quantities extracted from LQCD Strongly interacting massless partons P. Levai & U. Heinz PRC 57, 1879 (1998)

14. EoS of HG • Resonance gas model • all mesons of masses lighter than 1.5 GeV & all baryons of masses lighter than 2.0 GeV are considered in HG phase. • They are assumed to have constant masses and to be noninteracting.

15. Energy density and pressure

16. Isothermal lines on transverse plane at τ0=0.6 fm/c

17. Temperature profiles at various impact parameters

18. 2. 3. fireball expansion • Radial acceleration in central collision Parameterized to fit experimental data<pt> of π, K, p at freeze-out

19. Assuming isentropic expansion, s(τ)=s0*v0/V(τ)

20. Radial acceleration in non-central collision Parameter to fit experimental datav2 of π, K, p at freeze-out

21. b=9 fm,

22. Blast wave model

24. 3. Thermal properties of charmonia • Dissociation temperatures • Dissociation cross section in QGP and in HG

25. 3. 1. wavefunctions & binding energies & radii of charmonia at finite T Modified Cornell potential F. Karsch, M.T. Mehr, H. Satz, Z phys. C. 37, 617 (1988) σ=0.192 GeV2 : string tension α=0.471 : Coulomb-like potential constant μ(T) =√(Nc/3+Nf/6) gT : screening mass in pQCD In the limit μ(T)→0,

26. χc (1P) Ψ’(2S) J/ψ (1S) Screening mass 289 MeV 298 MeV 306 MeV 315 MeV 323 MeV 332 MeV 340 MeV GeV GeV GeV

27. Binding energies & radii of charmonia Radius (fm) Binding energy (GeV) Screening mass (MeV) Screening mass (MeV)

28. 3. 2. dissociation cross section • Bethe-Salpeter amplitude Definition ; Solution in NR limit ;

29. Leading Order (LO) quark-induced Next to Leading Order (qNLO)

30. gluon-induced Next to Leading Order (gNLO)

31. Leading Order (LO) quark-induced Next to Leading Order (qNLO) gluon-induced Next to Leading Order (gNLO)

32. In QGP σdiss=∑j σjpQCD 1. partons with thermal mass 2. temperature-dependent wavefunctions from modified Cornell potential are used. In hadronic matter Factorization formula: σdiss(p)=∑j ∫dx σipQCD(xp)Dj i(x) Dj i(x) is PDF of parton i in hadron j interacting with charmonia Massless partons mass factorization, loop diagrams and renormalization remove collinear, infrared and UV divergence respectively 2. Coulomb wavefunctions are used.

33. 4. Charmoniain heavy-ion collisions • Cronin effect • Nuclear absorption (nuclear destruction) • Thermal decay and leakage effect • Regeneration

34. Two-component model Kinetic freeze-out T≈ 120 MeV Thermalization (QGP formation) ≈ 0.6 fm/c Hadronization T≈ 170 MeV Before cc production Cronin effect Nuclear absorption Initial production of J/ψ through binary N-N collisions Thermal decay in QGP Thermal decay in hadronic matter detector Regenerated J/ψ Thermal decay in hadronic matter

35. 4. 1. Cronin effect • Charmonia are produced mainly through g+g fusion • Different from in p+p collision, gluon in A+B collision can get additional Pt through g+N collision • It broadens Pt distribution of gluons • Subsequently, it broadens Pt distribution of J/ ψ in A+B collision, compared with in p+p collision

36. Primordial J/ψ is produced Nucleus A Nucleus B

37. 4. 2. Nuclear destruction Primordial J/ψ is produced Nucleus A Nucleus B Nuclear destruction cross section is obtained from pA collision σdiss=1.5mb

38. 4. 3. Thermal decay J/ψ QGP phase J/ψ Mixed phase (Assuming 1st order phase transition) J/ψ HG phase

39. Thermal decay widths in QGP & HG

40. J/ψ (1S) χc (1P) Ψ’(2S)

41. The leakage effect Thermal decay width =0 Thermal decay width ≠0 Thermal decay width : Γ→Γ*θ[R(τ)-r(τ)]

42. Survival probability from thermal decay Considering feed-down from χc , Ψ’ to J/ψ,

43. 4. 4. Regeneration • From Glauber model (dσccNN/dy=63.7(μb) from pQCD), • From Statistical model, • Discrepancy between them is corrected with fugacity • GCE is converted to CE because of small # of pairs Canonical suppression

45. Relaxation factor for kinetic equilibrium

46. the number of regenerated J/ψ NJ/ψrec= VRγ2 {nJ/ψSJ/ψHG +Br(χc)*nχc *SχcHG + Br(ψ’) *nψ’* Sψ’HG } • nJ/ψ, nχc , nψ’ : number densities of charmonia • SJ/ψHG, SχcHG , Sψ’HG : survival rate of charmonia in HG • Br(χc), Br(ψ’) : branching ratios of χc,ψ’ to J/ψ • R : relaxation factor • γ : fugacity

47. 5. Results • RAA vs. Npart • RAA vs. pT • <pT> • V2 • Higher-order corrections in pQCD

48. 5. 1. RAA of J/ψ From RHIC near midrapidty at √sNN=200 GeV

49. RAA of J/ψ as a function of Npart(near midrapidity in Au+Au collision at √s=200 GeV) Regeneration

50. The role of coupling constant g in our model 1. ‘g’ determines dissociation temperatures of charmonia (screening mass μ=√(Nc/3+Nf/6) gT) TJ/ψ=386 MeV, Tχc =199 MeV, TΨ’=185 MeV with g=1.5 2. ‘g’ determines the thermal widths of charmonia (Г∼g2 in LO, and Г∼g4 in NLO) 3. ‘g’ determines the relaxation factor ofcharm quarks