Download - Approach to the High Density State of QCD
Approach to the High Density State of QCD
S. MuroyaTokuyama 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
J uly 10 (Thu)
9:15 - 9:25 Opening
9:25-10:40 Morning Session 1 (general overview)
9:25-10:10 Mark Alford
Dense quark matter in nature (incld. Review) 45min
10:10-10:40 Teiji Kunihiro
Some recent topics on possible chiral restoration in a nuclear medium (incld. Review) 30min
10:40-11:00 Coffee Break 20min
11:00-12:20 Morning Session 2 (Lattice, Review and 2-color QCD at finite density, simulations)
11:00-11:40 Maria-Paola Lombardo
Lattice QCD at finite density - Primer (incld. Review) 40min
11:40-12:20 Donald Sinclair Finite density lattice gauge theories with positive fermion determinants 40min
12:20 - 13:50 Lunch
13:50 - 14:40 Afternoon Session 1 (2-color QCD at finite density, simulations)
13:50-14:15 Shin Muroya Color SU(2) Lattice QCD High Density State 25min
14:15-14:40 J onivar Skullerud
Lattice simulations of 2-colour QCD with Wilson fermions 25min
14:40 - 15:30 Afternoon Session 2 (NJ L models at finite T and mu)
14:40-15:05 Costas Strouthos
The 3d NJ L 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
15:50 - 17:40 Afternoon Session 3 (Poster)
15:50-16:45 Five minutes presentation (11 posters)
Masakiyo Kitazawa
Pseudogap of color superconductivity
Hiroaki Abuki 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
Masaharu Iwasaki
Latent heat in the chiral phase transition
Chaejun Song Higher order calculation for CFL gap prefactor
Daiji Kimura NJ L 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
QCD at zero baryon density
Artan Borici Global Monte Carlo for light quarks
Hideko Nagahiro
$\ eta$ mesic nuclei in chiral models
Minoru Biyajima Description of $\ eta$-distributions at RHIC energies in terms of a stochastic model
16:45-17:45 Poster presentation
19:00 - 21:00 Banquet
J uly 11 (Fri) 9:15 - 10:55 Moring Session 1 (3-color QCD on the lattice, simulations)
9:15- 9:55 Zoltan Fodor
FINITE T/ MU LATTICE QCD AND THE CRITICAL POINT 40min
9:55-10:25 Sandor Katz
THE QCD EQUATION OF STATE AT FINITE T/ MU ON THE LATTICE 30min
10:25-10:50 Shinji Ejiri 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)
11:10-11:50 Frithjof Karsch Lattice QCD at non-zero chemical potential and t he resonance gas model 40min
11:50-12:20 Philippe de Forcrand
The phase diagram of three-flavor QCD for small baryon densities 30min
12:20 - 13:50 Lunch 13:50 - 15:30 Afternoon Session 1 (QCD phase structure: analytic approaches)
13:50-14:35 Misha Stephanov
QCD phase diagram and the critical point (incld. Review) 45min
14:35-15:00 Hirotsugu Fujii Soft Modes at the Critical End Point in the Chiral Effective Models 25min
15:00-15:30 Masayasu Harada
Vector Manifestation in Dense Matter 30min
15:30 - 15:50 Coffee Break 15:50 - 17:20 Afternoon Session 2 (various phases in high density matter, models)
15:50-16:30 Takumi Muto Meson Condensations in High Density Matter (Review) 40min
16:30-16:55 Toshitaka Tatsumi
Ferromagnetism and superconductivity in quark matter 25min
16:55-17:20 Aiichi Iwazaki Color Ferromagnetism and Quantum Hall St ates in Quark Matter 25min
18:30 - 19:30 Public Lecture Petersson at National Nara Museum
J uly 12 (Sat)
9:15 - 10:55 Morning Session 1 (Analytic approaches)
9:15- 9:55 Kenji Fukushima
Toward understanding recent lattice results from the strong coupling expansion 40min
9:55-10:25 Bengt Petersson
Dimensional Reduction 30min
10:25-10:55 Kei Iida 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)
11:15-11:45 Deog-Ki Hong
High Density Effective Theory of QCD 30min
11:45-12:15 Stephen Hsu Positivty and Dense Matter 30min
12:15-12:45 Motoi Tachibana
Neutrino processes in the $K 0̂$ condensed phase of color flavor locked quark matter 30min
12:45 - 14:15 Lunch 14:15 - 16:05 Afternoon Session 1 (Finite T and mu, simulations)
14:15-14:40 Peter Crompton
Comparing reweighting approaches to lattice QCD at finite baryondensities 25min
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
15:40-16:05 Olaf Kaczmarek
Heavy quark free energies, potentials and the renormalizedPolyakov Loop 25min
16:05 - 16:25 Coffee Break 16:25 - 17:50 Afternoon Session 2 (new directions)
16:25-16:55 J un Nishimura
A new Monte Carlo method for finite density QCD 30min
16:55-17:25 Harald Markum
Quantum Chaos in Supersymmetric QCD at Finite Density 30 min
17:25-17:50 summary/ closing
講演数42
Lattice MC
理論計算
QCD
モデル・アルゴリスム
SU(3)
SU(2)
QCD
NJL
Lattice
New Picture
12
2
6
2
8
6
6
20
22
http://www.riise.hiroshima-u.ac.jp/FDQCD/
Closing by Pierre van Baal
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
Critical end point?
2CS CFL
T
Big bang Universe
RHIC
GSI, J-PARC
hadron
QGP
sb sb
symmetry restore?
最近の標準的な相図
S. Takaki, PTP 109 (03)233
147MeV
=325MeV
(20,146)
2nd
2nd
1st
流体モデル を通じて実験と比較 (Asakawa and Nonaka)
臨界点付近での揺らぎが見えるか?
Critical end point?
2CS CFL
T
Big bang Universe
RHIC
GSI, J-PARC
hadron
QGP
sb sb
symmetry restore?
Does Chiral symmetry restore ? (m_s vs
s
Hiroaki Abuki : hep-ph/0306074
•Schwinger-Dyson eq, + CJT effective potential•Improved Ladder
_c =325 MeV by Takaki
Critical end point?
2CS CFL
T
Big bang Universe
RHIC
GSI, J-PARC
hadron
QGP
?
sb sb
symmetry never restore?
Does Chiral symmetry restore ? (m_s vs
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
4̂,'444̂,'44 )'()1(e)()1(e
xx
a
xx
a xUxU
3
1ˆ,'ˆ,'
)()1()()1(1i
ixxiiixxii xUxUW
GSedet1
e1 WODU
ZODDUD
ZO FG SS
• Introducing the chemical potential on a lattice (Wilson fermion)
• Phase (sign) problem
W U x U xx x x x
1 1 11
4
( ) ( ) ( ) ( )', ',
iPP 44
: hopping parameter quark mass
,WSF
Chemical Potential on a Lattice
)(e)( xiAxU
Tre e( ) ( ) H N S SDUD D G F
W W 5 5 complex:Wdet
iWW edetdet
Vi ee
Fodor-Katz, JHEP03(2002)014
MeV MeV 35725,5.3160 EET
12 FN2.0 ,025.0, sdu mm
8 ,6 ,4 ,43 ss NN
Standard gauge + Staggered fermion
Reweighting
OMDUZ
O gS )(e)(det1
OM
MMDU
Zggg SSS
)(det
)(dete)(dete
1
0
)()(0
)( 00
Fodor and KatzMulti-reweighting
method)( 0
)( 0
)(
)(
),,( m
• Allton et al. (Bielefeld-Swansea) hep-lat/0204010
Improved action + Improved staggered fermion
,2FN4163
0.2 ,1.0qmMeV
a=0.29
Taylor expansion at high T and low
Imaginary Chemical Potential
deForcrand and Philipsen NPB642(02)290; hep-lat/0307020
Im
)()( 210
I
IIC acca
D’Elia and Lombardo Phys.Rev. D67 (2003) 014505
At small )()(log 64
42
20 OaaaZ )()(log64
42
20 IIII OaaaZ ImI
complex:det M real:det M
ReIm i
Standard gauge + Staggered fermion
,2FN 250.0qm46 ,48 33
3
I Z(3) symmetry
Fodor-Katz
Allton et al.
deForcrand-Philipsen D’Elia and Lombardo
Consistent !? YES
• Effective theory• Finite Isospin
• Two-color QCD Pseudo-Real
du
)*,(det)(det WW 2
)(det)(det)(det WWW U U * 2 2
2*
2
24̂,'44*
4̂,'44*
3
1ˆ,'
*ˆ,'
*',2
*
);',(
'1e1e
)'()1()()1();',(
xxW
xUxU
xUxUxxW
xx
a
xx
a
iixxiiixxiixx
)'det);',(det)};',({det ** ;x'W(x,xxWxxW
detW:real Monte Carlo Calculation Works Well !
Models free from Sing Problem
Color SU(2) at Finite Density
0.01
0.1
1
10
100
0 1 2 3 4 5 6 7 8
RHO K160(periodic)
mu=0.0mu=0.1mu=0.2mu=0.3mu=0.4mu=0.5mu=0.6mu=0.7mu=0.8mu=0.9
G(n
t)
nt
0.001
0.01
0.1
1
10
100
0 1 2 3 4 5 6 7 8
Pi Kapp=160 (periodic)
mu = 0.0mu=0.1mu=0.2mu=0.3mu=0.4mu=0.5mu=0.6mu=0.7mu=0.8mu=0.9
G(n
t)
nt
4 X83
Clear evidence of meson mass decrease at finite chemical potential !
Color SU(2) at Finite Chemical Potential
Color SU(2) at Finite Chemical Potential
Peculiar behavior of a vector meson at finite density
Mass of becomes small ! Remind us of the CERES Experiment
a a=0.160 =0.175
Sinclare and Kogut, condensation with 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
Single-Particle DistributionsSingle-Particle Distributions
Hydro-dynamical model by Morita and Muroya
OutputOutput• Input ParametersInput ParametersEE0max0max = = 6.9 GeV/fm6.9 GeV/fm33 ( (TT00=238 MeV)=238 MeV)
<<EEiniini> => = 4.5 GeV/fm 4.5 GeV/fm33
nnB0B0 = = 0.31 fm0.31 fm-3-3
00++ = = 2.72.7
TTf f = = 130 MeV130 MeV
5.74 GeV/fm5.74 GeV/fm33
3.7 GeV/fm3.7 GeV/fm33
0.70 fm0.70 fm-3-3
1.091.09
EEff = 70 MeV/fm = 70 MeV/fm33
(<(<TTff> = 123 MeV)> = 123 MeV)
SPS Pb+PbSPS Pb+Pb
• OutputOutput
Total Energy = 37420 GeV (95%)Total Energy = 37420 GeV (95%)
Net Baryon Number = 256Net Baryon Number = 256
<<BB> = 110 MeV> = 110 MeV
<<vvTT> (|> (||<0.1) = 0.486|<0.1) = 0.486
3267 GeV (92%)3267 GeV (92%)
305305
280.2 MeV280.2 MeV
0.4670.467
Hydro-dynamical model by Morita and Muroya
RHIC 200Gev/A 17.8 GeV/A
Thomas Schafer,hep-ph/0304281
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 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
RHIC
JPARC
Ferro-Mgn.? Q-Hall st ?
http://www.riise.hiroshima-u.ac.jp/FDQCD/
Muroya, Nakamura, Nonaka and Takaishi : hep-lat/0306031