Introduction on sQGP and Bag model Gluon condensates in sQGP and in vacuum

1. Perturbative QCD apporach to Heavy quarkonium at finite temperature and density Su Houng Lee Yonsei Univ., Korea • Introduction on sQGP and Bag model • Gluon condensates in sQGP and in vacuum • J/y suppression in RHIC • Pertubative QCD approach for heavy quarkonium 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. Quark Gluon Plasma (T.D. Lee and E. Shuryak) Proton Proton At high T and/or Density Proton Nucleons in vacuum Quark Gluon Plasma

3. QCD Phase Diagram at finite T and r Quark Gluon Plasma (sQGP) ~ 170 MeV 0.17 / fm3 Lattice result: sudden change in p and E above Tc • Different • Particle spectrum (mass) • Vacuum • Deconfinement • Theoretical approach

4. Relativistic Heavy Ion collision Signal of QGP

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

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

7. Bag model and sQGP Outside pressure is balanced by confined quark pressure MIT Bag model : inside the Bag fvac=0, perturbative vacuume outside the Bag fvac = non zero , non perturbative vacuum Original bag model Later models

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

9. QCD vacuum vs. sQGP Vacuum with negative pressure Nonperturbative QCD vacuum sQGP MIT Bag • What is B in terms of QCD variables (operators) • Can understand soft modes associated with phase transition

10. Gluon condsenates in QGP and Vacuum

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

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

13. Gluon condensate in QGP from lattice calculation

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

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. J/y in QGP

18. J/y in Quark Gluon Plasma J/y melt above Tc Heavy quark potential on the lattice Karsch et al. (2000)

19. J/y suppression in Heavy Ion collision New RHIC data 1986: Matsui and Satz claimed J/y suppression is a signature of formation of Quark Gluon Plasma in Heavy Ion collision

20. J/y in Quark Gluon Plasma Quenched lattice calculation by Asakawa and Hatsuda using MEM T< 1.6 Tc T> 1.6 Tc J/y peak at 3.1 GeV 2003: Asakawa and Hatsuda claimed J/y will survive up to 1.6 Tc

21. Theoretical interpretations 1. C. H. Lee, G. Brown, M. Rho… : Deeply bound states 2. C. Y. Wong… : Deby screened potential • 1. Strong as at Tc < T < ~2 Tc • 2. J/y form Coulomb bound states at Tc < T < ~2 Tc

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

23. Progressin QCD calculations LO and NLO

24. Basics in Heavy Quark system 1. Heavy quark propagation Perturbative treatment are possible because

25. 2. System with two heavy quarks Perturbative treatment are possible when

26. Perturbative treatment are possible when

27. Historical perspective on Quarkonium Haron interaction in QCD • Peskin (79), Bhanot and Peskin (79) • a) From OPE • b) Binding energy= e0 >> L • Kharzeev and Satz (94,96) , Arleo et.al.(02,04) • a) Rederive, target mass correction • b) Application to J/y physics in HIC

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

29. NR Power counting in Heavy bound state 1. Perturbative part 2. External interaction: OPE

30. LO Amplitude

31. 2 1 3 Exp data However, near threshold, LO result is expected to have large correction mb s1/2 (GeV)

32. NLO Amplitude

33. q1 NLO Amplitude : Collinear divergence when q1=0. Cured by mass factroization

34. q1 q1 Integration of transverse momentum from zero to scale Q Mass factorization Gluons whose kcos q1 < Q scale, should be included in parton distribution function

35. NLO Amplitude : Higher order in g counting

36. NLO Amplitude : - cont Previous diagrams can be reproduced with effective four point vertex

37. Cancellation of infrared divergence Remaining Infrared Divergence cancells after adding one loop corrections

38. Application to Upsilon dissociation cross section Fit quark mass and coupling from fitting to coulomb bound state gives

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

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

41. Total cross section: gluon vs quark effects With thermal mq = mg = 200 MeV

42. Effective Thermal cross section: gluon vs quark effects

43. Effective Thermal width: gluon vs quark effects

44. Summary II • 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 realisticJ/y 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/y at finite temperature should be reliable.

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 • F. Klingl, S. Kim, S.H.Lee, P. Morath, W. Weise, PRL 82 (1999) 3396. • S.Kim and S.H.Lee, NPA 679 (2001) 517. • S.H.Lee and C.M. Ko, PRC 67 (2003) 038202. • 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 • Y.Oh, S.Kim and S.H.Lee, PRC 65 (2002) 067901. Additional 9. T.D. Lee, hep-ph/06 05017