1. Su Houng Lee 1. Quark condensate and the ’ mass 2. Gluon condensate and the Heavy quark system 3. Summary Medium dependence; are all hadrons alike? 1

2. 1. Quark condensate and the  ’ meson 2 1.Some introduction 2.Casher Banks formula 3.Lee-Hatsuda formula 4.Witten – Veneziano formula 5.At finite temperature and density

3. 3 Kapusta, Kharzeev, McLerran PRD 96 : Effective U(1) A restoration in medium in SPS data Some introduction Rapp, Wambach, van Hees: SPS dilepton data RHIC dilepton puzzle Csorgo, Vertesi, Sziklai : Additional contribution from  ’ mass reduction Experimental and theoretical works on  ‘ in nuclear medium QCD symmetry: SU(N) L x SU(N) R  SU(N) V and U(1) A is always broken by Anomaly QCD  confinement

4. 4 Finite temperature T/Tc  n 1 Quark condensate – Chiral order parameter Finite density Lattice gauge theory Linear density approximation

5. 5 Quark condensate Casher Banks formula - Chiral symmetry breaking (m  0)  Phenomenologically need constituent quark mass  Casher Banks formula in the chiral limit

6. 6 Other order parameters:  correlator (mass difference)  Phenomenologically constituent quark mass terms survives  Generalized Casher Banks formula in the chiral limit

7. 7 Correlation function for  ‘ (Lee, Hatsuda 96)  ‘  correlator (mass difference) =1  U(1) A symmetry will effectively be restored up to quark mass terms in SU(3) T. Cohen (96)Lee, Hatsuda (96)

8. 8 Contributions from glue only from low energy theorem When massless quarks are added Correlation function ’ mass? Witten-Veneziano formula - I Large Nc argument Need  ‘ meson

9. 9 Witten-Veneziano formula – II  ‘ meson Lee, Zahed (01)

10. 10 Large Nc counting Witten-Veneziano formula in medium (Kwon, Morita, Wolf, Lee in prep ) LET (Novikov, Shifman, Vainshtein, Zhakarov) at finite temperature for S(k): Ellis, Kapusta, Tang (98)

11. 11 LET at finite temperature for P(k) : Lee, Zahed (01) Therefore,

12. 12 W-V formula at finite temperature: Smoothes out temperature change because if Therefore, :  Observable consequences ?

13. 3. Heavy quark system 13 1.Charmonium system 2.Panda

14. 14 T/Tc s String Tension: QCD order parameter Early work on J/y at finite T (Hashimoto, Miyamura, Hirose, Kanki)

15. 15 J/y suppression in RHIC Matsui and Satz: J/y will dissolve at Tc due to color screening Lattice MEM : Asakawa, Hatsuda, Karsch, Petreczky, Bielefield, Nonaka…. J/y will survive Tc and dissolve at 2 Tc.. Still not settled at QM2011 Potential models (Wong …) :. Refined Potential models with lattice (Mocsy, Petreczky…) : J/y will dissolve slightly above Tc Lattice after zero mode subtraction (WHOT-QCD) : J/y wave function hardly changes at 2.3 Tc AdS/QCD (Kim, Lee, Fukushima, Stephanov…...) NRQCD: UK group+ S.Y. Kim QCD sum rule (Morita, Lee), QCD sum rule+ MEM (Gluber, Oka, Morita) Perturbative approaches: Blaizot et al… Imaginary potential pNRQCD: N. Brambial et al. Recent works on J/y in QGP

16. 16 AdS/QCD (Y.Kim, J.P.Lee, SHLee 07) J/J/  ’ Deconfinement Thermal effect? Mass (GeV)

17. 17 Perturbative treatment are possible because Heavy quark propagator

18. 18 Perturbative treatment are possible when Two Heavy quark propagator

19. 19 q2 q2 process expansion parameter example 0 Photo-production of open charm m 2 J/  > 0Bound state properties Formalism by Peskin (79) J/  dissociation: NLO J/  mass shift: LO -Q 2 < 0 QCD sum rules for heavy quarks Predicted m  c <m J/  before experiment Perturbative treatment are possible when

20. 20 At finite temperature: from Two independent operators Twist-2 Gluon Gluon condensate or T G0G0 G2G2 Lowest dimensional - Gluon operators

21. 21 W(ST)= exp(-  ST) Time Space S W(S-T) = 1- (ST) 2 +… W(S-S) = 1- (SS) 2 +… OPE for Wilson lines: Shifman NPB73 (80), vs confinement potential Local vs non local behavior W(SS)= exp(-  SS) T Behavior at T>Tc W(SS)= exp(-  SS) W(ST)= exp(- g(1/S) S) T

22. 22 Linear density approximation Condensate at finite density At  = 5 x  n.m. Operators in at finite density and hadronic phase

23. 23 Hatsuda, Adami, Brown.. (90) Lattice calculation (Lee 89) Non zero above Tc Non-perturbative Gluon condensate ; T Gluon condensate – Non perturbative Morita, Lee (08)

24. 24 In terms of density of eigenvalues Gluon condensate – Non perturbative

25. 25 Morita and Lee (08  present) In Vacuum In medium Heavy quark system – QCD sum rule constraints

26. 26  OPE for bound state: m  infinity Mass shift: QCD 2 nd order Stark Effect : Peskin 79  >  qcd  Attractive for ground state = T

27. 27 Summary of analysis Due to the sudden change of condensate near Tc T G0G0 G2G2 Abrupt changes for mass and width near Tc

28. 28 Melting of  ’ cc Slope:  J/  Melting T of J/  Height: mass of J/  RAA from RHIC (√s=200 GeV y=0, 2-comp model ( Rapp) Song, Park, Lee 10)

29. 29 Quantum numbers QCD 2 nd Stark eff. Potential model QCD sum rules Effects of DD loop  c 0 -+ –8 MeV–5 MeV (Klingl, SHL,Weise, Morita) No effect J/  1 -- –8 MeV (Peskin, Luke) -10 MeV (Brodsky et al). –7 MeV (Klingl, SHL,Weise, Morita) <2 MeV (SHL, Ko) c c 0,1,2 ++ -20 MeV-15 MeV (Morita, Lee) No effect on  c1  (3686) 1 -- -100 MeV (SHL, Ko) < 30 MeV  (3770) 1 -- -140 MeV (SHL, Ko) < 30 MeV Other approaches for mass shift in nuclear matter

30. 30 Anti proton Heavy nuclei Observation of  m through p-A reaction Expected luminosity at GSI 2x 10 32 cm -2 s -1 Can be done at J-PARC

31. 31  ’ mass is related to quark condensate and thus should reduce in medium  a) Could serve as signature of chiral symmetry restoration b) Dilepton in Heavy Ion collision c) Measurements from nuclear targets 2.Heavy quark system - related to confinement phenomena  a) Refined measurements in Heavy Ion collisions b) Measurements from nuclear target Summary

32. 32 Other order parameters:  correlator (mass difference)