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Su Houng Lee Theme: Relation between Quark condensate and the h ’ mass Ref:

Another look at h ‘ in medium. Su Houng Lee Theme: Relation between Quark condensate and the h ’ 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.

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Su Houng Lee Theme: Relation between Quark condensate and the h ’ mass Ref:

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  1. Another look at h‘ in medium Su Houng Lee Theme: Relation between Quark condensate and the h’ 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

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

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

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

  5. Other order parameters: s - pcorrelator (mass difference) Remember:

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

  7. UA(1) effect : effective order parameter (Lee, Hatsuda 96) • Topologically nontrivial contributions • h ‘- pcorrelator (mass difference) T. Cohen (96)

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

  9. h’ meson mass ? Witten – Veneziano formula At finite temperature and density

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

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

  12. Witten-Veneziano formula at finite T (Kwon, Morita, Wolf, Lee: PRD 12 ) • Large Nc counting • At finite temperature, only gluonic effect is important Glue Nc2 Quark Nc Quark Nc2 ?

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

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

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

  17. Summary • h’ 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. 2. In W-V formula h’ 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

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