the xxv international symposium on lattice field theory 29 july - 5 august 2007, regensburg,...
Post on 21-Dec-2015
213 views
TRANSCRIPT
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
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.
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
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 influencedby the chiral symmetry breaking.
Strong coupling LQCD does not suffer from the sign problem.
Previous studies
P4 Kohtaroh Miura, Talk in Lattice ‘07 on 070803
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
P5 Kohtaroh Miura, Talk in Lattice ‘07 on 070803
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)
P6 Kohtaroh Miura, Talk in Lattice ‘07 on 070803
Quark integral
Quark propagator
Derivation of meson mass I
P7 Kohtaroh Miura, Talk in Lattice ‘07 on 070803
SU(Nc) one link integralFaldt, Petersson (1986)
Differentiateby chiral condensate
Color SU(Nc) matrixQuark hopping in t-direction
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/FlavorsEnergy Meson mass
Meson species
=0 Meson mass spectrum
Meson mass spectrum
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)
Discussions
P10Kohtaroh Miura, Talk in Lattice ‘07 on 070803
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.
P11Kohtaroh Miura, Talk in Lattice ‘07 on 070803
LQCD action with
Seff [ ]
Hadron mass
Feff [ ]
Lattice spacing
Criticalvalues
Eq. of State
Phase diagram
Strong coupling LQCD
P12
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