1. Istanbul 06 S.H.Lee 1 1.Introduction on sQGP and Bag model 2.Gluon condensates in sQGP and in vacuum 3.J/  suppression in RHIC 4.Pertubative QCD approach for heavy quarkonium Perturbative QCD apporach to Heavy quarkonium at finite temperature and density Su Houng Lee Yonsei Univ., Korea Thanks to : Recent Collegues: C.M. Ko, W. Weise, B. Friman, T. Barnes, H. Kim, Y. Oh,.. Students: Y. Sarac, Taesoo Song, Y. Park, Y. Kwon, Y. Heo,..

2. Istanbul 06 S.H.Lee 2 At high T and/or Density Quark Gluon Plasma Proton Nucleons in vacuum Quark Gluon Plasma (T.D. Lee and E. Shuryak)

3. Istanbul 06 S.H.Lee 3 QCD Phase Diagram at finite T and  ~ 170 MeV 0.17 / fm 3 Quark Gluon Plasma (s QGP ) Different Particle spectrum (mass) Vacuum Deconfinement Theoretical approach Lattice result: sudden change in p and E above T c

4. Istanbul 06 S.H.Lee 4 Signal of QGP Relativistic Heavy Ion collision

5. Istanbul 06 S.H.Lee 5 Some highlights from RHIC Data from STAR coll. At RHIC Jet quenching: strongly interacting matter V2: very low viscosity

6. Istanbul 06 S.H.Lee 6 Vacuum property of sQGP MIT Bag model and Quark Gluon Plasma (QGP) sQGP  strongly interacting and very small viscosity

7. Istanbul 06 S.H.Lee 7 Bag model and sQGP MIT Bag model : inside the Bag  vac =0, perturbative vacuume outside the Bag  vac = non zero, non perturbative vacuum Original bag model Later models Outside pressure is balanced by confined quark pressure

8. Istanbul 06 S.H.Lee 8 Bag model and sQGP Phase transition in MIT Bag model Outside pressure is balanced by thermal quark gluon pressure Asakawa, Hatsuda PRD 97

9. Istanbul 06 S.H.Lee 9 QCD vacuum vs. sQGP MIT Bag Vacuum with negative pressure Nonperturbative QCD vacuum sQGP 1.What is B in terms of QCD variables (operators) 2.Can understand soft modes associated with phase transition

10. Istanbul 06 S.H.Lee 10 Gluon condsenates in QGP and Vacuum

11. Istanbul 06 S.H.Lee 11 Gluon condensate 1., dominated by non-perturbative contribution 2. RG invariant, gauge invariant, characteristic vacuum property, couples to spin 0 field 3. Can be calculated on the lattice (DiGiacomo et al. ) 5. Nucleon expectation value is 4. Related to trace of energy momentum tensor through trace anomaly (Hatsuda 87) 6. From we find

12. Istanbul 06 S.H.Lee 12 Gluon condensate in MIT Bag model Inside QGP Inside nucleon Using Explicit lattice calculation of non- perturbative gluon condensate?

13. Istanbul 06 S.H.Lee 13 Gluon condensate in QGP from lattice calculation

14. Istanbul 06 S.H.Lee 14 Lattice data show 1. Gluon condensate at T=0 is consistent with QCD sum rule value 2. Gluon condensate at T>Tc is 50 to 70 % of its vacuum value consistent with estimates of gluon condensate inside the Bag (nucleon) 3. The change occurs at the phase transition point T D Lee’s spin 0 field seems dominantly gluon condensate and their expectation value indeed changes similarly in Bag and QGP

15. Istanbul 06 S.H.Lee 15 QCD vacuum vs. sQGP MIT Bag Vacuum with negative pressure Nonperturbative QCD vacuum sQGP If phase transition occurs, there will be enhancement of massless glueball excitation

16. Istanbul 06 S.H.Lee 16 Summary I 1. Vacuum expectation value of Gluon condensate inside the Bag and QGP seems similar. sQGP is a large Bag  What will the viscosity be ?? What is the property of sQGP?  Physical consequence of phase transition? 2. Future GSI (FAIR) will be able to prove vacuum change through charmonium spectrum in nuclear matter

17. Istanbul 06 S.H.Lee 17 J/  in QGP

18. Istanbul 06 S.H.Lee 18 Karsch et al. (2000) Heavy quark potential on the lattice J/  in Quark Gluon Plasma J/  melt above T c

19. Istanbul 06 S.H.Lee 19 1986: Matsui and Satz claimed J/  suppression is a signature of formation of Quark Gluon Plasma in Heavy Ion collision J/  suppression in Heavy Ion collision New RHIC data

20. Istanbul 06 S.H.Lee 20 2003: Asakawa and Hatsuda claimed J/  will survive up to 1.6 T c Quenched lattice calculation by Asakawa and Hatsuda using MEM T< 1.6 T c T> 1.6 T c J/  peak at 3.1 GeV J/  in Quark Gluon Plasma

21. Istanbul 06 S.H.Lee 21 Theoretical interpretations 1. C. H. Lee, G. Brown, M. Rho… : Deeply bound states 2. C. Y. Wong… : Deby screened potential  1. Strong  s at T c < T < ~2 T c  2. J/  form Coulomb bound states at T c < T < ~2 T c

22. Istanbul 06 S.H.Lee 22 Became a question of quntative analysis a) What are the effects of Dynamical quarks ? b) What is the survial probability of J/  in QGP Relevant questions in J/  suppression  need to know J/  – gluon dissociation  need to know J/  – quark dissociation

23. Istanbul 06 S.H.Lee 23 Progress in QCD calculations LO and NLO

24. Istanbul 06 S.H.Lee 24 Basics in Heavy Quark system 1. Heavy quark propagation Perturbative treatment are possible because

25. Istanbul 06 S.H.Lee 25 2. System with two heavy quarks Perturbative treatment are possible when

26. Istanbul 06 S.H.Lee 26 q 2 process expansion parameter 0 Photo production of open charm -Q 2 < 0 QCD sum rules for heavy quarks m 2 J/  > 0 Dissociation cross section of bound states Perturbative treatment are possible when

27. Istanbul 06 S.H.Lee 27 Historical perspective on Quarkonium Haron interaction in QCD 1.Peskin (79), Bhanot and Peskin (79) a) From OPE b) Binding energy=  0 >>  2.Kharzeev and Satz (94,96), Arleo et.al.(02,04) a) Rederive, target mass correction b) Application to J/  physics in HIC

28. Istanbul 06 S.H.Lee 28 Rederivation of Peskin formula using Bethe-Salpeter equation (Lee,Oh 02) Resum Bound state by Bethe-Salpeter Equation

29. Istanbul 06 S.H.Lee 29 NR Power counting in Heavy bound state 1. Perturbative part 2. External interaction: OPE

30. Istanbul 06 S.H.Lee 30 LO Amplitude

31. Istanbul 06 S.H.Lee 31 1 2 3 However, near threshold, LO result is expected to have large correction mb s 1/2 (GeV) Exp data

32. Istanbul 06 S.H.Lee 32 NLO Amplitude

33. Istanbul 06 S.H.Lee 33 NLO Amplitude : 11 Collinear divergence when  1 =0. Cured by mass factroization

34. Istanbul 06 S.H.Lee 34 Mass factorization 11 Gluons whose kcos  1 < Q scale, should be included in parton distribution function Integration of transverse momentum from zero to scale Q 11

35. Istanbul 06 S.H.Lee 35 NLO Amplitude : Higher order in g counting

36. Istanbul 06 S.H.Lee 36 NLO Amplitude : - cont Previous diagrams can be reproduced with effective four point vertex

37. Istanbul 06 S.H.Lee 37 Cancellation of infrared divergence Remaining Infrared Divergence cancells after adding one loop corrections

38. Istanbul 06 S.H.Lee 38 Application to Upsilon dissociation cross section Fit quark mass and coupling from fitting to coulomb bound state gives

39. Istanbul 06 S.H.Lee 39 Total cross section for Upsilon by nucleon: NLO vs LO Large higher order corrections Even larger correction for charmonium NLO/LO

40. Istanbul 06 S.H.Lee 40 1. Large NLO correction near threshold, due to log terms 2. Dissociation by quarks are less than 10% of that by gluons  Thermal quark and gluon masses of 300 MeV will Reduce the large correction Quenched lattice results at finite temperature are reliable What do we learn from NLO calculation ?

41. Istanbul 06 S.H.Lee 41 Total cross section: gluon vs quark effects With thermal m q = m g = 200 MeV

42. Istanbul 06 S.H.Lee 42 Effective Thermal cross section: gluon vs quark effects

43. Istanbul 06 S.H.Lee 43 Effective Thermal width: gluon vs quark effects

44. Istanbul 06 S.H.Lee 44 Summary II 1.We reported on the QCD NLO Quarkonium-hadron dissociation cross section.  Large correction even for upsilon system, especially near threshold 2. The corrections becomes smaller with thermal quark and gluon mass of larger than 200 MeV  Obtained realistic J/  dissociation cross section by thermal quark and gluons 3. The dissociation cross section due to quarks are less than 10 % of that due to the gluons.  The quenched lattice calculation of the mass and width of J/  at finite temperature should be reliable.

45. Istanbul 06 S.H.Lee 45 Reference for part I Gluon condensates A. Di Giacomo and G. C. Rossi, PLB 100(1981) 481; PLB 1008 (1982) 327. Su Houng Lee, PRD 40 (1989) 2484. Charmonium in nuclear matter 3.F. Klingl, S. Kim, S.H.Lee, P. Morath, W. Weise, PRL 82 (1999) 3396. 4.S.Kim and S.H.Lee, NPA 679 (2001) 517. 5.S.H.Lee and C.M. Ko, PRC 67 (2003) 038202. 6.S.J.Brodsky et al. PRL 64 (1990) 1011 Quarkonium hadron interaction 7. M.E. Peskin, NPB 156 (1979) 365; G.Bhanot and M. E. Peskin, NPB156 (1979) 391 8.Y.Oh, S.Kim and S.H.Lee, PRC 65 (2002) 067901. Additional 9. T.D. Lee, hep-ph/06 05017