1. Su Houng Lee Quark condensate and the ’ mass  ‘ at finite temperature 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. 13  ’ 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 Summary

14. 14 Other order parameters:  correlator (mass difference)