Approach to
the High Density State of
QCD
S. Muroya
Tokuyama Women’s College
Contents
•
•
•
•
•
•
Introduction
Finite Density QCD in Naraの話題
理論から予想される相図
格子シミュレーションの現状
実験に寄せる期待
まとめ
物理学最前線 “クォークマター” 宮村修 1986
物理学最前線 “クォークマター” 宮村修
物理学最前線 “クォークマター” 宮村修
Program
July 10 (Thu)
15:50 - 17:40 Afternoon Session 3 (Poster)
9:15 - 9:25 Opening
15:50-16:45 Five minutes presentation (11 posters)
9:25-10:40 Morning Session 1 (general overview)
Mark
9:25-10:10
Alford
10:10-10:40
Teiji
Kunihiro
Dense quark matter in nature (incld. Review) 45min
Some recent topics on possible chiral restoration in a
nuclear medium (incld. Review) 30min
11:00-12:20 Morning Session 2 (Lattice, Review and 2-color QCD at finite density,
simulations)
Maria-Paola
Lombardo
11:40-12:20 Donald Sinclair
Lattice QCD at finite density - Primer (incld.
Review) 40min
Finite density lattice gauge theories with positive
fermion determinants 40min
Improved Schwinger-Dyson approach to pairing phenomena and
QCD phase diagram
Satoshi Takagi
Phase Structure of Hot and/or Dense QCD in the
Schwinger-Dyson Approach
13:50 - 14:40 Afternoon Session 1 (2-color QCD at finite density, simulations)
Higher order calculation for CFL gap prefactor
Daiji Kimura
NJL Model at Finite Chemical Potential in a Constant Magnetic
Field
Yusuke Nishida
Thermodynamics of strong coupling 2-color QCD with chiral and
diquark condensates
Slavo
Kratochvila
Hideko
Nagahiro
Minoru Biyajima
13:50-14:15 Shin Muroya
14:15-14:40
Jonivar
Skullerud
Color SU(2) Lattice QCD High Density State 25min
Lattice simulations of 2-colour QCD with Wilson
fermions 25min
Latent heat in the chiral phase transition
Chaejun Song
Artan Borici
12:20 - 13:50 Lunch
Pseudogap of color superconductivity
Hiroaki Abuki
Masaharu
Iwasaki
10:40-11:00 Coffee Break 20min
11:00-11:40
Masakiyo
Kitazawa
QCD at zero baryon density
Global Monte Carlo for light quarks
$\eta$ mesic nuclei in chiral models
Description of $\eta$-distributions at RHIC energies in terms of a
stochastic model
16:45-17:45 Poster presentation
19:00 - 21:00 Banquet
14:40 - 15:30 Afternoon Session 2 (NJL models at finite T and mu)
14:40-15:05
Costas
Strouthos
The 3d NJL model at nonzero temperature and density
25min
15:05-15:30 David N Walters A BCS Gap on the lattice 25min
15:30 - 15:50 Coffee Break
July 11 (Fri)
July 12 (Sat)
9:15 - 10:55 Moring Session 1 (3-color QCD on the lattice, simulations)
Zoltan
FINITE T/MU LATTICE QCD AND THE CRITICAL POINT
9:15- 9:55
Fodor
40min
9:15 - 10:55 Morning Session 1 (Analytic approaches)
Kenji
Toward understanding recent lattice results from the
9:15- 9:55
Fukushima
strong coupling expansion 40min
9:55-10:25
Sandor
Katz
THE QCD EQUATION OF STATE AT FINITE T/MU ON
THE LATTICE 30min
Study of QCD thermodynamics at finite density by Taylor
expansion 25min
10:50 - 11:10 Coffee Break
11:10 - 12:20 Morning Session 2 (3-color QCD on the lattice, simulations, continued)
Lattice QCD at non-zero chemical potential and t he
11:10-11:50 Frithjof Karsch
resonance gas model 40min
10:25-10:50 Shinji Ejiri
Philippe de
The phase diagram of three-flavor QCD for small
11:50-12:20
Forcrand
baryon densities 30min
12:20 - 13:50 Lunch
13:50 - 15:30 Afternoon Session 1 (QCD phase structure: analytic approaches)
Misha
QCD phase diagram and the critical point (incld.
13:50-14:35
Stephanov
Review) 45min
14:35-15:00 Hirotsugu Fujii
Soft Modes at the Critical End Point in the Chiral
Effective Models 25min
Masayasu
Vector Manifestation in Dense Matter 30min
Harada
15:30 - 15:50 Coffee Break
15:50 - 17:20 Afternoon Session 2 (various phases in high density matter, models)
Meson Condensations in High Density Matter (Review)
15:50-16:30 Takumi Muto
40min
9:55-10:25
10:25-10:55 Kei Iida
Toshitaka
Tatsumi
16:55-17:20 Aiichi Iwazaki
Ferromagnetism and superconductivity in quark matter
25min
Color Ferromagnetism and Quantum Hall St ates in
Quark Matter 25min
18:30 - 19:30 Public Lecture
Petersson at National Nara Museum
Dimensional Reduction 30min
Ginzburg-Landau approach to color superconductivity
30min
10:55-11:15 Coffee Break
11:15 - 12:45 Morning Session 2 (effective theory and color superconfuctivity)
Deog-Ki
11:15-11:45
High Density Effective Theory of QCD 30min
Hong
11:45-12:15 Stephen Hsu Positivty and Dense Matter 30min
Motoi
Neutrino processes in the $K^0$ condensed phase of
Tachibana
color flavor locked quark matter 30min
12:45 - 14:15 Lunch
14:15 - 16:05 Afternoon Session 1 (Finite T and mu, simulations)
Peter
Comparing reweighting approaches to lattice QCD at
14:15-14:40
Crompton
finite baryondensities 25min
12:15-12:45
14:40-15:10
Sourendu
Gupta
Stepping off the wall--- Taylor expansions in the
chemical potential 30min
15:10-15:40
Tetsuya
Takaishi
Hadronic property at finite density -- results from
QCD-TARO projects -- 30min
15:00-15:30
16:30-16:55
Bengt
Petersson
Olaf
Heavy quark free energies, potentials and the
Kaczmarek
renormalizedPolyakov Loop 25min
16:05 - 16:25 Coffee Break
16:25 - 17:50 Afternoon Session 2 (new directions)
Jun
16:25-16:55
A new Monte Carlo method for finite density QCD 30min
Nishimura
15:40-16:05
16:55-17:25
17:25-17:50
Harald
Markum
Quantum Chaos in Supersymmetric QCD at Finite
Density 30 min
summary/closing
講演数４２
SU(3)
12
SU(2)
2
QCD
Lattice MC
理論計算
モデル・アルゴリスム
6
Lattice
2
QCD
8
NJL
6
New Picture
6
http://www.riise.hiroshima-u.ac.jp/FDQCD/
20
22
お土産のマグカップの
シンボルマーク
by 湯川先生
将来の会議で
シンボルマークに
使われるであろう
初田さんの 書
バンケットの主役
中村さんの
パンフルート
Closing by
Pierre van Baal
最近の標準的な相図
Big bang
Universe
T
QGP
RHIC
Critical end point？
GSI, J-PARC
hadron
csb
2CS
csymmetry restore?
CFL
csb
m
2nd
(20,146)
147MeV
2nd
1st
=325MeV
S. Takaki, PTP 109 (03)233
臨界点付近での揺らぎが見えるか？
流体モデル を通じて実験と比較
(Asakawa and Nonaka)
Does Chiral symmetry restore ? (m_s vs m)
Big bang
Universe
T
QGP
RHIC
Critical end point？
GSI, J-PARC
hadron
csb
2CScs
csymmetry restore?
CFL
csb
m
Hiroaki Abuki : hep-ph/0306074
m_c =325 MeV
by Takaki
•Schwinger-Dyson eq, + CJT effective potential
•Improved Ladder
Does Chiral symmetry restore ? (m_s vs m)
Big bang
Universe
T
QGP
RHIC
Critical end point？
GSI, J-PARC
hadron
csb
2CS ?
CFL
csb
c-symmetry never restore? m
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
Chemical Potential on a Lattice
• Introducing the chemical potential on a lattice
(Wilson fermion)
Tre - ( H - mN ) DUD D e - ( SG S F )
U m ( x) e
iAm ( x )
S F W , W 1 - (1 - m )U m ( x) x ', x m (1 m )U m ( x) x ', x - m
4
m 1
：hopping parameter
P4 P4 - im
3
quark mass
W 1 - (1 - i )U i ( x) x ', x iˆ (1 i )U i ( x) x ', x -iˆ
i 1
W 5W 5
- e ma (1 - 4 )U 4 ( x) x ', x4ˆ e-ma (1 4 )U 4 ( x' ) x ', x-4ˆ
det W : complex
• Phase (sign) problem
1
1
O DUD DO e - SG - S F DU O det W e -SG
Z
Z
i
det W det W e
e i e -V
Fodor-Katz, JHEP03(2002)014
TE 160 3.5 MeV , mE 725 35 MeV
Standard gauge
+ Staggered fermion
NF 2 1
mu,d 0.025, ms 0.2
Ns3 4, Ns 4, 6, 8
Reweighting
1
-Sg ( )
O DU det M ( ) e
O
Z
1
- S g ( 0 )
S g ( 0 ) - S g ( ) det M ( )
DU e
det M ( 0 ) e
O
Z
det M ( 0 )
Fodor and Katz
Multi-reweighting
method
( 0 )
( )
( , m, m )
( 0 )
( )
Taylor expansion at high T and low m
• Allton et al. (Bielefeld-Swansea) hep-lat/0204010
Improved action
+ Improved staggered fermion
170 MeV
N F 2, mq 0.1, 0.2
163 4
ma=0.29
Imaginary Chemical Potential
deForcrand and Philipsen NPB642(02)290; hep-lat/0307020
D’Elia and Lombardo Phys.Rev. D67 (2003) 014505
At small m
log Z (m ) a0 a2 m 2 a4 m 4 O(m 6 )
det M : complex
mI
3
m I Im m
log Z ( m I ) a0 - a2 m I a4 m I O( m I )
2
det M : real
Z(3) symmetry
Im m -i Re m
C (am I ) c0 c1 (am I ) 2
m I Im m
Standard gauge
N F 2, mq 0.025
3
3
+ Staggered fermion 8 4, 6 4
4
6
Allton et al.
Fodor-Katz
Consistent !?
YES
deForcrand-Philipsen
D’Elia and Lombardo
Models free from Sing Problem
• Effective theory
• Finite Isospin
mu -md
det W ( m ) det W (- m ) det W ( m )
det W (-m ) det W (m )*,
Um* 2Um2
• Two-color QCD 3
Pseudo-Real
W ( x, x' ; m )* 2 x , x ' - (1 - *i )U i ( x) x ', x iˆ (1 *i )U i ( x' ) x ', x -iˆ
i 1
)
)
- e ma 1 - *4 U 4 x ) x ', x 4ˆ e - ma 1 *4 U 4 x') x ', x -4ˆ 2
2W ( x, x' ; m* ) 2
{det W ( x, x' ; m )}* det W ( x, x' ; m* ) det W(x, x' ; 'm )
detW:real
Monte Carlo Calculation Works Well !
2
Color SU(2) r at Finite Density
3
4 X8 , 0.160
mu = 0.0
mu=0.1
mu=0.2
mu=0.3
100
mu=0.4
mu=0.5
mu=0.6
mu=0.7
10
mu=0.8
mu=0.9
Pi Kapp=160 (periodi c)
100
10
G(nt)
G(nt )
1
0.1
mu=0.0
mu=0.1
mu=0.2
mu=0.3
mu=0.4
mu=0.5
mu=0.6
mu=0.7
mu=0.8
mu=0.9
RHO K160( periodic)
r
1
0.1
0.01
0.001
0.01
0
1
2
3
4
nt
5
6
7
8
0
1
2
3
4
5
nt
Clear evidence of r meson mass decrease
at finite chemical potential !
6
7
8
Color SU(2)
r at Finite Chemical Potential
Peculiar behavior of a vector meson at finite density
=0.160
a
=0.175
Mass of r becomes small !
Remind us of the CERES Experiment
a
Sinclare and Kogut,
condensation with m_I
diquark condensation in colorSU(2)
Talk by Fukushima.
Strong coupling expansion works well to investigate Lattice results
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
Hydro-dynamical model by Morita and Muroya
Single-Particle Distributions
Output
RHIC 200Gev/A
• Input Parameters
E0max = 6.9 GeV/fm3 (T0=238 MeV)
<Eini> = 4.5 GeV/fm3
nB0 = 0.31 fm-3
h0+h = 2.7
Tf
= 130 MeV
17.8 GeV/A
SPS Pb+Pb
5.74 GeV/fm3
3.7 GeV/fm3
0.70 fm-3
1.09
Ef = 70 MeV/fm3
(<Tf> = 123 MeV)
• Output
Total Energy = 37420 GeV (95%)
Net Baryon Number = 256
<mB> = 110 MeV
<vT> (|h|<0.1) = 0.486
3267 GeV (92%)
305
280.2 MeV
0.467
Hydro-dynamical model by Morita and Muroya
高密度QCD
•複雑な相構造
•Strange quark mass の違い
異なった Symmetry breaking pattern
• model の入れ方が重要
Tatsumi, Iwasaki et al,, , もっといろいろな可能性も
•Lattice simulation for small m seems to work enough
•Future experiments at GSI and/or JPARC
に期待しみんなで応援しましょう
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 ?
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