T ～1012K Hot matter： ρ ～ 1012 kg/cm3Dense matter：

Neutronliquid

QuarkMatter?

Lattice QCD confronts experiments

Japanese-German Seminar 2010 Nov. 6 (2010) at Mishima

T. Hatsuda (University of Tokyo)

Many-body Problems in QCD

1. Introduction to QCD phase structure

2. Hot QCD confronts RHIC/LHC experiments

3. Dense QCD confronts neutron star observations

4. Dense QCD confronts ultracold atomic experiments ?

5. Summary

Recent review:

“The Phase Diagram of Dense QCD”K. Fukushima and T. Hatsuda, Rep. Prog. Phys. 73 (2010)

arXiv: 1005.4814 [hep-ph]

contents

Symmetry realization in hot/dense QCD（for mu,d,s=0 case）

QGP

BRLC USUSUSU )1(])3()3([)3(

QGP :

Cabibbo & Parisi, PLB 59 (1975)Collins & Perry, PRL 34 (1975)

0 Rt

RL

t

L CqqCqqCFL :

Alford, Rajagopal & Wilczek, NPB 537 (1999)

RLRLC ZZSU )2()2()3(

cSB :

Nambu, PRL 4 (1960)

BRLC USUSU )1()3()3(

0RLqq

QCD vs. condensed matters

cSB CSC

QGP

1. Competition between different orders

2. Strong coupling

Common features

• Kitazawa, Nemoto, Kunihiro, PTP (‘02)

• Abuki, Itakura & Hatsuda, PRD (’02)

• Chen, Stajic, Tan & Levin, Phys. Rep. (’05) Dirac

Fermi

Transition at Finite T

cSB CSC

QGP

Chiral field: ~

Chiral transformation:

Pisarski & Wilczek (‟84)

Symmetry:

Ginzburg-Landau-Wilson analysis in hot QCD

SU(Nf)LxSU(Nf)RxU(1)A

SU(Nf)LxSU(Nf)R

quark mass term

Axial anomaly

X

AfNZ )2(

Pisarski and Wilczek, PRD29 (‟84)

Svetitsky & Yaffe, NPB210 (‟82)Order of the thermal QCD transition (μ=0)

1st

1st

cross over

2nd

ms

small

larg

e

m u,dsmall large

Nf=0

Nf=1

Nf=2

Nf=3

Transition at Finite T

cSB CSC

QGP

Asakawa-Yazaki CP

by T.D.Lee Tsinghua University, Beijing (photo by G. Baym)

Relativistic Heavy Ion Collisions

particle

productionFreezeoutthermalization QGP hydrodynamic

expansion

RHIC & LHC

PHENIX@RHIC STAR@RHIC ALICE@LHC

Hot QCD confronts RHIC/LHC experiments

Theoretical Inputs

for equation of state

for local correlations

・ Lattice QCD・ pＱＣＤ・ AdS/QCD

Relativistic hydrodynamics

for space-time evolution

∂μTμν =0

Laudau (1953), Namiki & Iso (1957)・ 1D hydro by Bjorken (1983) ・ 3D hydrodynamics by

Hirano, Muroya, Nonaka (2000-)

lepton

hadron

jet

charm

bottom

photon

Initial energy density

Energ

y D

ensity

(GeV

/fm

3 )

AGS

SPS

RHIC

c.m. energy / nucleon

(GeV)

Lattice QCD

3D hydrodynamics with lattice EOS

http://www.youtube.com/watch?v=p8_2TczsxjMby T. Hirano

http://www.youtube.com/watch?v=p8_2TczsxjM

・ State-of-the-art lattice EOS・ Full 3D hydrodynamics・ Experimental SPF at T=0

Akamatsu, Hatsuda, Hamagaki, & Hirano (2010)

Dilepton emission with lattice EOS

Predictions for LHC

Hirano, Huovinen and Nara,arXiv:10106222 [nucl-th] Nov.1 (2010)

・State-of-the-art lattice EOSgiven by HOT QCD Coll.

・Full 3D hydrodynamics+ hadron cascade

Transition at finite μ

cSB CSC

QGP

CP

Neutronliquid

QuarkMatter?

Nuclear Force and Neutron Star

(ρmax ～ 6ρ0)

PSR1913+16

Neutron star binary

Pressure balance

gravity

Repulsive core

Fermi pressure

Oppenheimer-Volkov(1939)

NN

NNN

Ozel, Baym & Guver, arXiv: 1002.3153 [astro-ph.HE]Steiner, Luttimer & Brown, arXiv: 1005.0811 [astro-ph.HE]

From TOV to EOS

M-R relation fromthermonuclear Burst in X-ray Binaries

Color superconductivity

major differences from the standard BCS superconductor

1. Relativistic fermi system

color-magnetic int. dominant High Tc : Tc/eF ~ 0.1

Compact pair : r~ 1-10 fm

2. Color-flavor entanglementVarious phases (c.f. Ice, 3He)

2SC, uSC, dSC, CFL etc

flavor color

u

d s

u

d s

u

d s

u

d s

CFLdSCuSC2SC

Pisarski & Wilczek, PRD29 (‟84) Iida & Baym, PRD63 (‟01) Yamamoto, Tachibana, Baym & Hatsuda, PRL97 (‟06)

GL analysis for chiral-super interplay in QCD (Nf=3)

Symmetry:

Chiral field: diquark field:

AZ )6(

Complete classification of the GL potential (mu,d,s=0)Yamamoto, Tachibana, Baym & Hatsuda, PRL 97 (‟06), PRD 76 („07)

Axial anomaly

RL ZZ )2()2( broken explicitly

Chiral-CFL interplay in Nf=3

Natural parameter relations

phase diagram (without d-σ coupling)

μ

T

phase diagram (with d-σ coupling)

Low T critical point driven by the axial anomaly

T

μ

phase diagram (with d-σ coupling & quark mass)

h

Low T critical point driven by the axial anomalyHigh T critical point driven by Higgs condensate

T

μ

Critical points from symmetry point of view

Original idea : Hatsuda and Alford (2010)

Figure taken fromSchmitt, Stetina & Tachibana, arXiv: 10104243 [hep-ph]

Spectral continuity at finite μ

cSB CSC

QGPCP induced by Higgs

CP induced by anomaly

mco

ndensa

tes

Continuity in the ground state

Generalized Gell-Mann-Oakes-Renner relation :

Yamamoto, Tachibana, Baym & T.H., PR D76 (‟07)

○

Tachibana, Yamamoto and T.H.,PRD78 (2008)

○

Continuity in excitation modes

Vector meson – CFL gluon continuity (QCD sum rules):

diquark

BCS

Baryon

BCSdiquark

BEC

Dense QCD confronts UCA experiments?

“Simulating dense QCD matter with Ultracold atoms”Maeda, Baym and Hatsuda, Phys. Rev. Lett. 103 (2009) 085301

Neutron

matter

quark

Matter?

Ultracold Atoms (UCA)

・T ~ 10-7 K

・hyperfine states

magnetically controllable

・density 1014 - 1015 cm-3

( cf. Air ~ 1019cm-3 )

10 12

10 9

10 7

T[K]

10 2

10

1

10 -3

10 -7

Quark-gluon plasma

Superfluid neutron matter

Center of sun

Boiling waterFreezing water

Liquid nitrogen

Superfluid, superconductor

Superfluid of 3He

Ultracold atoms

Neutron

matter

quark

Matter?

b fσ

s-wave boson-fermion

scattering length

strong weak

0

Maeda, Baym and Hatsuda, Phys. Rev. Lett. 103 (2009) 085301Atomic Boson-Fermion mixture

Induced superfluidity of composite fermions

-- a novel analogy between cold atoms and QCD --

Maeda, Baym & Hatsuda,Phys. Rev. Lett. 103 (‟09)

Composite

Fermion

cold atoms dense QCD

weak (bf)-(bf) attraction ⇔ strong b-f attraction baryon superfluidity ⇔ strong diqark correlation

Y. Nambu, Nobel Lecture (Dec.8, 2008), page 24/25

1. QCD phase structure・ Three major phases in QCD: χSB, QGP and CSC

・ Axial anomaly plays crucial roles everywhere

・ Close similarity to high Tc supercond. & multi-comp. cold atoms

2. Chiral-super interplay driven by axial anomaly・ A new critical point at low T and high μ

・ Continuity of χSB phase and CSC phase

3. Spectral continuity in high density QCD・ Pions are pions.

・ Vector mesons are gluons.

4. Near future・ Hot QCD confront LHC experiments

・ Dense QCD confronts neutron star observations

・ Dense QCD confronts ultracold atomic experiments

Summary and Future

1. QCD phase structure・ Three major phases in QCD: χSB, QGP and CSC

・ Axial anomaly plays crucial roles everywhere

・ Close similarity to high Tc supercond. & multi-comp. cold atoms

2. Chiral-super interplay driven by axial anomaly・ A new critical point at low T and high μ

・ Continuity of χSB phase and CSC phase

3. Spectral continuity in high density QCD・ Pions are pions.

・ Vector mesons are gluons.

4. Near future・ Hot QCD confront LHC experiments

・ Dense QCD confronts neutron star observations

・ Dense QCD confronts ultracold atomic experiments

Summary and Future

RHIC/LHC

LQCD Neutron

stars

UCA