1. Analysis of transverse momentum dependence of J/ψ in Heavy-Ion Collisions Xingbo Zhao with R. Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA 24 th WWND, Apr. 10 2008

2. 2 Outline 1.p T dependence for two-component model 2.Numerical results for SPS and RHIC 3. Study of R AA (p T ) at high p T 4. Summary and outlook

3. 3 1.0) 2-Component Model Boltzmann Transport Equation satisfies the homogenous equation where is from (p T indep.) with initial condition = ~

4. 4 1.1) p T dependence of direct component 1.Cronin effect from p-A data at SPS at SPS(RHIC) at RHIC [Hüfner et. al. 01’]

5. 5 1.1) p T Dependence of Direct Component 2. Momentum dependence of dissociation rate : cylindrically expanding fireball with entropy conservation QGP Stage: i. Gluo-dissociation: Ineffective for small ii. Quasi-free: adjust to R AA (E T ) at SPS Hadronic Stage: SU(4) effective theory, rate is small [Bhanot and Peskin 79’] [Grandchamp and Rap 01’]

6. 6 1.1)p T Dependence of Dissociation Rate Numerical results of rates [Rapp 05’]

7. 7 1.1) Leakage Effect 3.Leakage Effect Charmonia with high p T may travel out of fireball before freeze out and are therefore effectively subject to less suppression. [Blaizot and Ollitrault ’88, Karsch and Petronzio 88, Zhuang and Hüfner 01]

8. 8 1.2) p T Dependence of Coalescence Component Blastwave approximation: evaluated at hadronization transition, (same fireball as for direct component) at RHIC(SPS) [Schnedermann et. al. 93’] = ~

9. 9 1.3) Two Parameters and Two parameters adjusted to R AA (N part ) of J/ψ 1. in Quasifree cross section adjust to R AA (N part ) at SPS NA50 (Alternatively gluodiss. is used with of J/ψ) 2. Time delay in statistical equilibrium limit from R AA (N part ) at RHIC AuAu [Braun-Munzinger et. al. 00’] [Grandchamp and Rapp 02’]

10. 10 2.1) R AA (E T ) and (E T ) at SPS Coalescence comp. small,  s fit by suppression Slight reduction of due to quasifree dissociation in QGP

11. 11 2.2) R AA (N part ) and (N part ) at RHIC See also [Thews 05’],[Yan et.al. 06’],[Andronic et.al. 07’]

12. 12 2.3) R AA (p T ) of J/ψ for RHIC AuAu

13. 13 2.4) Elliptic Flow for J/ψ from AuAu at RHIC v 2 is small for all p T

14. 14 3) Study of R AA (p T ) at high p T Increasing trend of R AA (p T >5 GeV)

15. 15 3.0) 4 Attempts to improve R AA (p T >5GeV) 1.Sensitivity on Cronin effect ( ) ? 2.B->J/ψ? 3.Formation time effect? 4.Gluo-dissociation rate in QGP stage?

16. 16 3.1) Sensitivity on Weak constraint for Cronin effect from d+Au at RHIC

17. 17 3.2) B->J/ψ R AA (p T ) from B feeddown increase at high p T

18. 18 3.3) Formation Time Effect Effectively smaller dissociation for high p T Charmonium :Nuclear absorption, Partonic and Hadronic Suppression Rate :Formation time of Charmonia J/ψ χ c Ψ’ τ form (fm/c) 0.89 2.01 1.50 [Gavin and Vogt 90’, Blaizot and Ollitrault 88’, Karsch and Petronzio 88’]

19. 19 3.3) Formation Time Effect

20. 20 3.4) Gluo-dissociation rate in QGP stage

21. 21 4) Summary and Outlook Rate equation approach including suppression and regeneration for J/psi, chi_c and psi’ Two paramters (  s and ) can reproduce centrality dependence at SPS and RHIC Resulting pt dependence consistent with data up to pt~5 GeV Extra ingredients needed at high pt (formation time, B feeddown, Cronin) Next : Full Boltzmann Equation with more microscopic charm quark distributions Check In-Medium physics in more detail: lattice QCD……

22. 22 Thank you! (Details can be found in hep-ph/0712.2407, accepted by PLB)