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, (2012) SHL, S. Cho, IJMP E 22 (2013) U A (1) breaking effects and  ‘ at finite temperature 1

2 QCD Lagrangian ‘ mass, Chiral symmetry restoration and UA(1) effect ? Usual vacuumFinite T a 1    ‘ ? ? mass

3 CBELSA/TAPS coll Experimental evidence of property change of ‘ in matter ? 1. Only a small increase in width in nuclear matter; cf vector mesons 2. May be some indirect evidence from RHIC; T. Csorgo et al. 3. Lattice result ?

Correlators and symmetry 4 1. Correlators can be related to experimental observables 2. Chiral symmetry breaking in Correlator 3. U A (1) breaking effects in Correlators Cohen 96Hatsuda, Lee 96

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

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

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

Correlators and symmetry 8 1. Correlators can be related to experimental observables 2. Chiral symmetry breaking in Correlator 3. U A (1) breaking effects in Correlators Cohen 96Hatsuda, Lee 96

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

10  ‘  correlator (mass difference) =1  For 2 point function, U(1) A symmetry will effectively be broken for N F 3 Lee, Hatsuda (96) For N-point U(1) A will be broken for N F < N  so what happens to the  ‘ mass?

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

12 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

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

14 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 ?

15 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

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

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

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

19  ’ 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 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 ? Generalization to Nuclear medium possible

Summary 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

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