1. The XXV International Symposium on Lattice Field Theory 29 July - 5 August 2007, Regensburg, Deutschland K. Miura, N. Kawamoto and A. Ohnishi Hokkaido University, Japan Kawamoto, Miura, Ohnishi, Ohnuma, Phys.Rev.D75:014502,2007 P1 Meson spectrum in the SU(Nc) phase of finite T & mu in SC-LQCD Ohnishi et al. hep-lat/0701024 Ohnishi et al. arXiv:0704.2823 Refs.

2. Table of Contents P2 1: Introduction * Motivations 2: Formulations * Derivation of meson mass in SC-LQCD 3: Results * Analytic expression of meson masses * mu dependence of meson mass 4: Summary Kohtaroh Miura, Talk in Lattice ‘07 on 070803

3. Motivations P3 Kohtaroh Miura, Talk in Lattice ‘07 on 070803 What’s the thermodynamic property of meson mass under the chiral phase transition at high T and mu ? Meson mass derivation in SC-LQCD at high T and mu system Monte-Carlo simulation does not work well for large chemical pot. systems because of a sign problem. It is suggested that the chiral phase transition takes place at high T and large mu. Meson masses are crucially influenced by the chiral symmetry breaking. Strong coupling LQCD does not suffer from the sign problem.

4. Previous studies P4 Kohtaroh Miura, Talk in Lattice ‘07 on 070803 1 species staggered fermion in SC-LQCD. Damgaard-Kawamoto-Shigemoto(‘85) Damgaard-Hochberg-Kawamoto(‘85) Bilic-Karsch-Redlich(‘92) Azcoiti-Di Carlo-Galante-Laliena(03) Nishida-Fukushima-Hatuda(‘04) Nishida(‘04) Kawamoto-Miura-Ohnishi-Ohnuma(‘05) T Baryon There are many studies investigating the meson masses in the SC-LQCD (Kawamoto and Smit, (1981) etc…). But there is no work considering meson mass with T and mu. The effective free energy has been derived for the finite T and mu case in the SC-LQCD. CSC U(Nc) SU(3) SU(Nc) SU(2) SU(3) color

5. Starting point P5 Kohtaroh Miura, Talk in Lattice ‘07 on 070803 Lattice QCD action(1 species of staggered fermion) strong coupling limit Temperature Anti-periodic boundary condition for fermions Temporal gauge for gluons: c.f. Hasenfratz-Karsch(‘83)

6. Introduction of chiral cond. 1/d expansion Auxiliary Field (Chiral condensate) P6 Kohtaroh Miura, Talk in Lattice ‘07 on 070803 Quark integral Quark propagator

7. Derivation of meson mass I P7 Kohtaroh Miura, Talk in Lattice ‘07 on 070803 SU(Nc) one link integral Faldt, Petersson (1986) Differentiate by chiral condensate Color SU(Nc) matrix Quark hopping in t-direction

8. Derivation of meson mass II P8 Kohtaroh Miura, Talk in Lattice ‘07 on 070803 Equilibrium of “B” Coefficient of (fluctuation)^2 c.f. Kluberg-Stern et al. (1983) for (T, mu)=0 systems Doublers/Flavors EnergyMeson mass Meson species =0 Meson mass spectrum

9. P9 Kohtaroh Miura, Talk in Lattice ‘07 on 070803 Nishida, Phys.Rev.D69:094501 (2004) Kawamoto, Miura, Ohnishi, Ohnuma, Phys.Rev.D75:014502,2007 Effective free energy Meson mass Input and output minimum search of c.f. Faldt, Petersson, Nucl. Phys. B264 (1986)

10. Discussions P10 Kohtaroh Miura, Talk in Lattice ‘07 on 070803 Chiral lim. PCAC relation Meson mass variation for mu Chiral lim. T=Tc(0)/2

11. Summary We derived an analytic expressions of meson masses with respect to the function of T and mu in the strong coupling limit of lattice QCD. Meson masses decrease quickly when the chemical pot. approaches to the critical value. P11 Kohtaroh Miura, Talk in Lattice ‘07 on 070803

12. LQCD action with S eff [ ] Hadron mass F eff [ ] Lattice spacing Critical values Eq. of State Phase diagram Strong coupling LQCD P12 S eff [ ] Link integral 1/d, 1/g^2 expansion Auxiliary fields, etc. MFA, Matusbara sum Minimum search Mass fitting Kohtaroh Miura, Talk in Lattice ‘07 on 070803 Present Expected to do Expected to improve Minimum search