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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. 講演数42. SU(3). 12. QCD. 20. SU(2). - PowerPoint PPT Presentation
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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