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Meson spectrum in the SU(Nc) phase of finite T & mu in SC-LQCD

Meson spectrum in the SU(Nc) phase of finite T & mu in SC-LQCD. 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. Refs.

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Meson spectrum in the SU(Nc) phase of finite T & mu in SC-LQCD

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  1. Meson spectrum in the SU(Nc) phase of finite T & mu in SC-LQCD 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 Refs. Kawamoto, Miura, Ohnishi, Ohnuma, Phys.Rev.D75:014502,2007 Ohnishi et al. arXiv:0704.2823 Ohnishi et al. hep-lat/0701024 P1

  2. Table of Contents 1: Introduction* Motivations2: Formulations * Derivation of meson mass in SC-LQCD3: Results* Analytic expression of meson masses * mu dependence of meson mass4: Summary Kohtaroh Miura, Talk in Lattice ‘07 on 070803 P2

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

  4. Previous studies 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 color Baryon T 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) U(Nc) SU(3) SU(Nc) SU(Nc) SU(2) SU(3) SU(3) Kohtaroh Miura, Talk in Lattice ‘07 on 070803 P4 1 species staggered fermion in SC-LQCD.

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

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

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

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

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

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

  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. Kohtaroh Miura, Talk in Lattice ‘07 on 070803 P11

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

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