Approach to the High Density State of QCD

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Approach to the High Density State of QCD

• S. Muroya
• Tokuyama Womens College

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Contents

• Introduction
• Finite Density QCD in Nara???
• ???????????
• ?????????????
• ????????
• ???

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???42
SU(3)
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QCD
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SU(2)
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Lattice MC
?????????
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2
Lattice
QCD
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????
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NJL
New Picture
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http//www.riise.hiroshima-u.ac.jp/FDQCD/
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?????????? ??????? by ????
?????? ???????? ???????? ????? ?
???????? ????? ??????
Closing by Pierre van Baal
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?????????
QGP
Critical end point?
T
hadron
CFL
2CS
csb
csb
m
csymmetry restore?
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2nd
(20,146)
147MeV
2nd
1st
325MeV
S. Takaki, PTP 109 (03)233
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????????????????
????? ????????? (Asakawa and Nonaka)
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Does Chiral symmetry restore ? (m_s vs m)
QGP
Critical end point?
T
hadron
CFL
2CS
cs
csb
csb
m
csymmetry restore?
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Hiroaki Abuki hep-ph/0306074
m_c 325 MeV by Takaki

• Schwinger-Dyson eq, CJT effective potential
• Improved Ladder

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Does Chiral symmetry restore ? (m_s vs m)
QGP
Critical end point?
T
hadron
?
2CS
CFL
csb
csb
m
c-symmetry never restore?
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Approach to high density state of the Lattice QCD

• Reweighting method
• Fodor Katz
• Grasgow
• Taylor expansion
• Imaginary Chemical Potential
• Density of the state
• Positive Measure model

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Chemical Potential on a Lattice

• Introducing the chemical potential on a lattice
• (Wilson fermion)
• Phase (sign) problem

khopping parameter quark mass
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Fodor-Katz, JHEP03(2002)014
Standard gauge Staggered fermion
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Reweighting

• Fodor and Katz
• Multi-reweighting
• method

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Taylor expansion at high T and low m

• Allton et al. (Bielefeld-Swansea) hep-lat/0204010

Improved action Improved staggered fermion
170 MeV
ma0.29
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Imaginary Chemical Potential
deForcrand and Philipsen NPB642(02)290
hep-lat/0307020
DElia and Lombardo Phys.Rev. D67 (2003) 014505

• At small m

Z(3) symmetry
Standard gauge Staggered fermion
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Allton et al.
Fodor-Katz
Consistent !? YES
deForcrand-Philipsen
DElia and Lombardo
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Models free from Sing Problem

• Effective theory
• Finite Isospin
• Two-color QCD Pseudo-Real

Monte Carlo Calculation Works Well !
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Color SU(2) r at Finite Density
, k 0.160
r
p
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Color SU(2) r at Finite Chemical Potential

• Peculiar behavior of a vector meson at finite
  density

k0.175
k0.160
a
a

• Mass of r becomes small !
• Remind us of the CERES Experiment

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• Sinclare and Kogut,
• p condensation with m_I
• diquark condensation in colorSU(2)

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Talk by Fukushima. Strong coupling expansion
works well to investigate Lattice results
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Where exists a high density state?

• Quark star ?
• Compact star etc
• Something new cosmological object?
• Collision experiment
• CERES/NA45 Pb-Au 40GeV/A
• spectrum change is clearer than 200GeV/A
• GSI or J-PARC 50 GeV/A

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Single-Particle Distributions
Hydro-dynamical model by Morita and Muroya
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Output
17.8 GeV/A
RHIC 200Gev/A
SPS PbPb

• Input Parameters

5.74 GeV/fm3 3.7 GeV/fm3 0.70 fm-3 1.09 Ef 70
MeV/fm3 (ltTfgt 123 MeV)
E0max 6.9 GeV/fm3 (T0238 MeV) ltEinigt 4.5
GeV/fm3 nB0 0.31 fm-3 h0sh 2.7 Tf
130 MeV

• Output

Total Energy 37420 GeV (95) Net Baryon Number
256 ltmBgt 110 MeV ltvTgt (hlt0.1) 0.486
3267 GeV (92) 305 280.2 MeV 0.467
Hydro-dynamical model by Morita and Muroya
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• ???QCD
• ??????
• Strange quark mass ??? ???? Symmetry
  breaking pattern
• model ???????
• Tatsumi, Iwasaki et al,, , ????????????
• Lattice simulation for small m seems to work
  enough
• Future experiments at GSI and/or JPARC
• ???????????????

http//www.riise.hiroshima-u.ac.jp/FDQCD/
RHIC
Muroya, Nakamura, Nonaka and Takaishi
hep-lat/0306031
JPARC
Thomas Schafer, hep-ph/0304281
Ferro-Mgn.? Q-Hall st ?