1. Su Houng Lee Theme: 1.Will U A (1) symmetry breaking effects remain at high T/  2.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 Meson in matter 1

2. 2 QCD Lagrangian ‘ mass, Chiral symmetry restoration and UA(1) effect ? Usual vacuumChiral sym restored a 1    ‘ ? ? mass

3. 3 CBELSA/TAPS coll Experimental evidence of property change of ‘ in matter ? Nanova et al. 1. Imaginary part: Transparency ratio 2. Real part: Excitation function + momentum distribution of the meson

4. Correlators and symmetry 4 1. Chiral symmetry breaking in Correlator 2. U A (1) breaking effects in Correlators Cohen 96 Hatsuda, Lee 96

5. 5 Finite temperature T/Tc  n 1 Quark condensate – Chiral order parameter Finite density Lattice gauge theory Linear density approximation

6. 6 Quark condensate Chiral symmetry breaking (m  0) : order parameter  Casher Banks formula:  Chiral symmetry breaking order parameter

7. 7 Other order parameters:  correlator

8. 8 Other order parameters: V - A correlator (mass difference)

9. 9 Meson with one heavy quark : S-P Baryon sector :  –  *

10. Correlators and symmetry 10 1. Chiral symmetry breaking in Correlator 2. U A (1) breaking effects in Correlators Cohen 96 Hatsuda, Lee 96

11. 11 U A (1) effect : effective order parameter (Lee, Hatsuda 96)  ‘  correlator : = 0 part T. Cohen (96) Topologically nontrivial contributions

12. 12  ‘  correlator : nonzero part =1 Lee, Hatsuda (96) For SU(3) : =1 For SU(2) : Always non zero For N-point function: U(1) A will be restored with chiral symmetry for N > N F but always broken for N < N F

13. 13 Recent Lattice results ? 1.S. Aoki et al. (PRD 86 11451) : no UA(1) effect above Tc 2.M. Buchoff et al. (PRD89 054514): UA(1) effect survives Tc in SU(2) in susceptibilities  But what happens to the  ‘ mass?  What is the relation to chrial symmetry Chiral symmetry restoration UA(1) symmetry restoration ? chiral UA(1)

14. Correlators and  ’ meson mass 14 1. Witten – Veneziano formula 2. At finite temperature and density

15. 15 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

16. 16 Witten-Veneziano formula – II  ‘ meson Lee, Zahed (01) Should be related to at m  0 limit

17. 17 Few Formula in Large Nc Meson Glueball Baryon

18. 18 Witten-Veneziano formula – III Nc counting and glueball  ‘ meson  ‘ mass is a large 1/N c correction glueball

19. 19 Witten-Veneziano formula – IV Low energy theorem is a Non-perturbative effect  ‘ mass is a large 1/N c correction

20. 20 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 ?

21. 21 Large Nc argument for Nucleon Scattering Term Witten That is, scattering terms are of order N c and can be safely neglected

22. 22 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

23. 23 LET (Novikov, Shifman, Vainshtein, Zhakarov) at finite temperature : Ellis, Kapusta, Tang (98) Lee, Zahed (2001)

24. 24 at finite temperature Therefore, when chiral symmetry gets restored

25. 25 W-V formula at finite temperature: Smooth temperature dependence even near Tc Therefore,  eta’ mass should decrease at finite temperature

26. 26 CBELSA/TAPS coll Experimental evidence of property change of ‘ in matter ? 10 % reduction of mass from around 400 MeV from chiral symmetry breaking

27. 27  ’ correlation functions should exhibit symmetry breaking from N-point function in SU(N) flavor even when chiral symmetry is restored.  For SU(2), UA(1) effect will be broken in the two point function Summary 2. In W-V formula  ’ mass is related to quark condensate and thus should reduce at finite temperature independent of flavor due to chiral symmetry restoration  a) Could serve as signature of chiral symmetry restoration b) Dilepton in Heavy Ion collision c) Measurements from nuclear targets seems to support it ?

28. Summary 28 1. Chiral symmetry breaking in Correlator 2. U A (1) breaking effects in Correlators  Restored in SU(3) and real world 3. WV formula suggest mass of  ‘ reduces in medium and at finite temperature: due to chiral symmetry restoration 4. Renewed interest in Theory and Experiments both for nuclear matter and at may be at finite T