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