1. J/  nuclear modification factor in nucleus-nucleus collisions Xiao-Ming Xu

2. outline a brief review of J/  mechanisms in medium J/  nuclear modification factor in nucleus- nucleus collisions summary J/  and the critical point

3. fundamental processes stimulated by SPS

4. dissociation in QGP T. Matsui, H. Satz, Phys. Lett. B178 (1986) 416 color screening M.E. Peskin, Nucl. Phys. B156 (1979) 365 G. Bhanot, M.E. Peskin, Nucl. Phys. B156 (1979) 391 D. Kharzeev, H. Satz, Phys. Lett. B334 (1994) 155

5. dissociation in hadronic matter (1) constant cross sections J/  + hadron  charmed mesons (charmed baryons) Dissociation cross sections of J/  in collisions with hadrons are assumed to be independent of the center- of-mass energy of J/  and hadron. J. Ftacnik et al., Phys. Lett. B207 (1988) 194 S. Gavin et al., Phys. Lett. B207 (1988) 257 R. Vogt et al., Phys. Lett. B207 (1988) 263 C. Gerschel et al., Phys. Lett. B207 (1988) 253

6. dissociation in hadronic matter (2) quark model calculations J/  + hadron  charmed mesons (charmed baryons) Barnes-Swanson quark-interchange model The dissociation cross sections depend on the center- of-mass energy of J/  and hadron. K. Martins et al., Phys. Rev. C51 (1995) 2723 C.-Y. Wong et al., Phys. Rev. C65 (2001) 014903 T. Barnes et al., Phys. Rev. C68 (2003) 014903 X.-M. Xu et al., Nucl. Phys. A713 (2003) 470

7. Prior form: gluon propagation before quark interchange

8. Post form: gluon propagation after quark interchange

9. dissociation in hadronic matter (3) meson exchange model calculations J/  + hadron  charmed mesons (charmed baryons) hadronic effective Lagrangians The dissociation cross sections depend on the center-of- mass energy of J/  and hadron. S.G. Matinyan, B. Muller, Phys. Rev. C58 (1998) 2994 K.Haglin, Phys. Rev. C61 (2000) 031902 Z. Lin, C.M. Ko, Phys. Rev. C62 (2000) 034903 ············

11. fundamental processes stimulated by RHIC

12. recombination mechanism X.-M. Xu, Nucl. Phys. A658 (1999) 165 P. Braun-Munzinger, J. Stachel, Phys. Lett. B490 (2000) 196 R.L. Thews, M. Schroedter, J. Rafelski, Phys. Rev. C63 (2001) 054905 

13. Spectral function analysis in quenched QCD dissociation temperature of > 1.5T c dissociation temperature of ~ 1.1T c M. Asakawa, T. Hatsuda, Phys. Rev. Lett. 92 (2004) 012001

14. Challenge: Can we discover a new mechanism for J/  at LHC?

15. Model predictions on J/  produced in nucleus-nucleus collisions X.-M. Xu, Nucl. Phys. A697 (2002) 825

16. history of high-energy nucleus-nucleus collisions AA QGM (no T) QGP HM 1 2 3 5

17. history of high-energy nucleus-nucleus collisions 1. initial nucleon-nucleon collisions; 2. thermalization of quark-gluon matter; 3. evolution of quark-gluon plasma; 4. hadronization at a critical temperature; 5. evolution of hadronic matter until freeze-out.

18. production of is a pointlike color singlet or a color octet pair from is produced in the initial nuclear collisions, during the thermalization of quark-gluon matter, in the evolution of quark-gluon plasma.

19. recombination In quark-gluon matter probability for to form a bound state J/  (  cJ,  ´) is proportional to the product of the NRQCD nonperturbative matrix elements and a medium modification factor.

20. NRQCD nonperturbative matrix elements  Ο 8 H ( 3 S 1 )  = constant,  Ο 8 H ( 1 S 0 )  = constant,  Ο 8 H ( 3 P 0 )  = constant Ο 8 H ( 3 S 1 )=χ + σT a ψ · (a + H a H )ψ + σT a χ Ο 8 H ( 1 S 0 )=χ + T a ψ (a + H a H ) ψ + T a χ ψ the field that annihilates a heavy quark. χ the field that creates a heavy antiquark.

21. medium modification factors S-wave color-octet state P-wave color-octet state medium: quark-gluon matter (no T and T) cross section

22. dissociation penetrates through deconfined matter and hadronic matter, interacts with partons in deconfined matter interacts with hadrons in hadronic matter

23. two definitions Charmonium is prompt if the point at which the charmonium state is produced and the collision point of the colliding beams cannot be resolved using a vertex detector. A charmonium coming from the decay of b-hadrons is not prompt. Charmonium is direct if the charmonium is prompt but does not come from the decay of a higher charmonium state. The prompt J/  includes direct J/  as well as the radiative feeddown from direct  cJ and direct .

24. = short-distance production  recombination  dissociation charmonium from initial nuclear collisions charmonium from prethermal stage charmonium from thermal stage

25. p T - and y- spectra Momentum distribution of J/  : produced via recombination during the thermalization of quark-gluon matter and in the evolution of quark-gluon plasma cause enhancement of J/  in some momentum region. ratio: The ratio is the J/  nuclear modification factor.

26. left: p T distribution  J/   right: rapidity distribution

27. ratio versus p T at y=0, central Au-Au collisions, 200GeV

28. ratio versus rapidity at p T =4 GeV/c, central Au-Au collisions, 200GeV

29. nuclear modification factors for high-p T J/  in Cu-Cu collisions --- from Hugo Pereira Da Costa’s talk PHENIX Minimum BiasSTAR + PHENIX Central collisions

30. nuclear modification factors for high-p T J/  in Au-Au collisions --- from Duncan Prindle’ talk Au+Au: 0-80% Star preliminary

31. SUMMARY (1) Mechanisms: dissociation and recombination. (2) Has the study of J/  at both SPS and RHIC accomplished the discovery of mechanisms for J/  in nucleus-nucleus collisions? (3) Competition between charmonium dissociation and charmonium formed from charm quarks and antiquarks in deconfined matter. (4) J/  enhancement in some momentum region

32. Suggest J/  as a probe of the critical point Reason: On one side of the critical point, confined matter, no recombination of charm quark and charm antiquark. On the other side of the critical point, deconfined matter, recombination of charm quark and charm antiquark. The nuclear modification factor of J/  is affected by the recombination. Method: 1. system size dependence of R AA 2. beam energy dependence of R AA

33. Find a critical point in Fig. 5 of Phys. Rev. Lett. 98, 232301 (2007)

37. Azimuthal Asymmetry of J/  Production X.-N. Wang, F. Yuan, Phys. Lett. B540 (2002) 62 J/  is affected only by v 2 ( p T =3 GeV, N P =130 )  0.022 at RHIC Z.W. Lin, D. Molnar, Phys. Rev. C68 (2003) 044901 V. Greco, C.M. Ko, R. Rapp, Phys. Lett. B595 (2004) 202 L. Yan, P. Zhuang, N. Xu, Phys. Rev. Lett. 97 (2006) 232301 J/  is affected by dissociation and recombination