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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
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

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Table of contents
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

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Motivations
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

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Previous studies
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

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1 species staggered fermion in SC-LQCD.


Starting point
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

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Introduction of chiral cond
Introduction of chiral cond.

1/d expansion

Auxiliary Field (Chiral condensate)

Quark integral

Quark propagator

Kohtaroh Miura, Talk in Lattice ‘07 on 070803

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Derivation of meson mass i
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


Derivation of meson mass ii
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

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Kohtaroh Miura, Talk in Lattice ‘07 on 070803


Meson mass spectrum
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

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Discussions
Discussions

PCAC relation

Chiral lim.

Meson mass variation for mu

Chiral lim.

T=Tc(0)/2

Kohtaroh Miura, Talk in Lattice ‘07 on 070803

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Summary
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

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Strong coupling lqcd
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

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