1. Su Houng Lee Theme: Relation between Quark condensate and the ’ mass Ref: SHL, T. Hatsuda, PRD 54, R1871 (1996) Y. Kwon, SHL, K. Morita, G. Wolf, PRD86,034014 (2012) SHL, S. Cho, IJMP E 22 (2013) 1330008 Another look at  ‘ in medium 1

2. Correlators and Quark condensate 2 1.Some introduction 2.Casher Banks formula 3.Lee-Hatsuda formula

3. 3 Finite temperature T/Tc  n 1 Quark condensate – Chiral order parameter Finite density Lattice gauge theory Linear density approximation

4. 4 Quark condensate Chiral symmetry breaking (m  0) : order parameter  Casher Banks formula:  Chiral symmetry breaking order parameter

5. 5 Other order parameters:  correlator (mass difference) Remember:

6. 6 Other order parameters: V - A correlator (mass difference)

7. 7 U A (1) effect : effective order parameter (Lee, Hatsuda 96)  ‘  correlator (mass difference) T. Cohen (96) Topologically nontrivial contributions

8. 8  ‘  correlator (mass difference) =1  U(1) A symmetry will effectively be restored in two point functions up to quark mass terms in SU(3) Lee, Hatsuda (96) Note three point functions sensitive to U(1) A symmetry will remain broken N-point function will be always broken for SU(N) flavor.  so what happens to the  ‘ mass?

9.  ’ meson mass ? 9 1.Witten – Veneziano formula 2.At finite temperature and density

10. 10 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

11. 11 Witten-Veneziano formula – II  ‘ meson Lee, Zahed (01) Should be related to at m  0 limit

12. 12 Large N c counting Witten-Veneziano formula at finite T (Kwon, Morita, Wolf, Lee: PRD 12 ) At finite temperature, only gluonic effect is important Glue N c 2 Quark N c Quark N c 2 ?

13. 13 Large Nc argument for Meson Scattering Term Witten That is, scattering terms are of order 1 and can be safely neglected WV relation remains the same

14. 14 LET (Novikov, Shifman, Vainshtein, Zhakarov) at finite temperature for S(k): Ellis, Kapusta, Tang (98)

15. 15 at finite temperature Therefore, when chiral symmetry gets restored Cohen 96

16. 16 W-V formula at finite temperature: Smooth temperature dependence even near Tc Therefore, :  eta’ mass should decrease at finite temperature

17. 17  ’ correlation functions should exhibit symmetry breaking from N-point function in SU(N) flavor even when chiral symmetry is restored.  For SU(3), the two point function will become symmetric. Summary 2. In W-V formula  ’ mass is related to quark condensate and thus should reduce at finite temperature  a) Could serve as signature of chiral symmetry restoration b) Dilepton in Heavy Ion collision c) Measurements from nuclear targets ? Generalization to Nuclear medium possible