The XXV International Symposium on Lattice Field Theory 29 July - 5 August 2007, Regensburg, Deutschland K. Miura, N. Kawamoto and A. Ohnishi Hokkaido.

The XXV International Symposium on Lattice Field Theory 29 July - 5 August 2007, Regensburg , Deutschland

K. Miura, N. Kawamoto and A. OhnishiHokkaido University, Japan

Kawamoto, Miura, Ohnishi, Ohnuma, Phys.Rev.D75:014502,2007

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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.

Table of Contents

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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

Motivations

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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 influencedby the chiral symmetry breaking.

Strong coupling LQCD does not suffer from the sign problem.

Previous studies

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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 massesin 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(Nc)SU(2)SU(3)SU(3)

color

Starting point

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Lattice QCD action(1 species of staggered fermion)

strong coupling limit

TemperatureAnti-periodic boundary condition for fermionsTemporal gauge for gluons:

c.f. Hasenfratz-Karsch(‘83)

Introduction of chiral cond.1/d expansion

Auxiliary Field (Chiral condensate)

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Quark integral

Quark propagator

Derivation of meson mass I

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SU(Nc) one link integralFaldt, Petersson (1986)

Differentiateby chiral condensate

Color SU(Nc) matrixQuark hopping in t-direction

Derivation of meson mass II

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Equilibrium of “B”

Coefficient of (fluctuation)^2

c.f. Kluberg-Stern et al. (1983) for (T, mu)=0 systems

Doublers/FlavorsEnergy Meson mass

Meson species

=0 Meson mass spectrum

Meson mass spectrum

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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)

Discussions

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Chiral lim.

PCAC relation

Meson mass variation for mu

Chiral lim.T=Tc(0)/2

Summary

We derived an analytic expressions of meson masseswith respect to the function of T and mu in the strongcoupling limit of lattice QCD.

Meson masses decrease quickly when the chemical pot. approaches to the critical value.

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LQCD action with

Seff [ ]

Hadron mass

Feff [ ]

Lattice spacing

Criticalvalues

Eq. of State

Phase diagram

Strong coupling LQCD

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Seff [ ]

Link integral1/d, 1/g^2 expansion

Auxiliary fields, etc.

MFA, Matusbara sum

Minimumsearch

Mass fitting

Kohtaroh Miura, Talk in Lattice ‘07 on 070803

PresentExpected to doExpected to improve

Min

imum

searc

h