T. Hatsuda (University of Tokyo)

QCD Phase StructureQCD Phase Structure

at High Baryon Density at High Baryon Density

contents• Introduction • Ginzburg-Landau approach to Dense QCD (1)

• Continuity in Dense QCD (2,3)

• UCA/QCD Correspondence (4)

• Summary

(1) Tachibana, Yamamoto, Baym & T.H., PRL 97 (2006) 122001; PRD 76 (2007) 074001.

(2) Tachibana, Yamamoto & T.H., PRD 78 (2008) 011501.

(3) Maeda, Baym and T.H., PRL 103 (2009) 085301

(4) Abuki, Baym, Yamamoto and T.H., arXiv: 1003.0408 [hep-ph]

NFQCD, March 10, 2010

Physics Today, Dec. vol.58 (2005)

http://www.lsbu.ac.uk/water/phase.html H2O H2O

4He 4He

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

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

QGP

0 RtRL

tL CqqCqqCFL :

Alford, Rajagopal & Wilczek, NP B537 (1999)

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

QGP :

Collins & Perry, PRL 34 (1975)

SB :

Nambu, PRL 4 (1960)

BRLC USUSU )1()3()3( RLRLC ZZSU )2()2()3(

0RLqq

QCD and high temperature superconductivityQCD and high temperature superconductivity

SB 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　　

SB CSC

QGP

Chiral field: ~

Chiral transformation:

Pisarski & Wilczek (’84)

Symmetry:

Ginzburg-Landau-Wilson analysis in hot QCD Ginzburg-Landau-Wilson analysis in hot QCD

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

SU(Nf)LxSU(Nf)R

quark mass term

Axial anomaly

XAfNZ )2(

Pisarski and Wilczek, PRD29 (’84)

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

1st

1st

cross over

2nd

ms

small

larg

e

mu,dsmall large

Nf=0

Nf=1

Nf=2

Nf=3

Transition at Finite T　　

SB CSC

QGP

Asakawa-Yazaki CP

Transition at finite μ　　

SB CSC

QGP

CP

Thermonuclear Burst in X-ray Binaries4U 1608-248 EXO 1745-248 4U 1820-30

Mass-Radius relation of Neutron Stars and dense EOS Mass-Radius relation of Neutron Stars and dense EOS

1

42

2 21

R

GM

fD

RA

c

2/1

2

21

4

R

GM

D

GMF

csedd

(i) Apparent surface area

(ii) Eddington limit

Ozel, Baym & Guver, arXiv: 1002.3153 [astro-ph.HE]

Color superconductivity at high densityColor superconductivity at high density

major differences from the standard BCS superconductor

1. Relativistic fermi system color-magnetic int. dominant

High Tc : Tc/F ~ 0.1Compact pair : r~ 1-10 fm

Son, PRD59 (’99), Schafer & Wilczek, PRD60 (’99)Pisarski & Rischke, PRD61 (’00)Hong, Miransky, Shovkovy & Wijewardhana, PRD61 (’00)

2. Color-flavor entanglement

Various 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 & T.H., PRL97 (’06)

GL analysis for chiral-super interplay in QCD (Nf=3) 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)Complete classification of the GL potential (mu,d,s=0)Yamamoto, Tachibana, Baym & T.H., PRL 97 (’06), PRD 76 (‘07)

Axial anomaly

RL ZZ )2()2( broken explicitly

Chiral-CFL interplay in NChiral-CFL interplay in Nff=3 =3

Natural parameter relations

phase diagram (without d-σphase diagram (without d-σ coupling)coupling)

μ

T

phase diagram (with d-σ coupling)phase diagram (with d-σ coupling)

Low T critical point driven by the axial anomalyLow T critical point driven by the axial anomaly

T

μ

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

h

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

T

μ

NJL model with axial anomaly (mu=md=ms) NJL model with axial anomaly (mu=md=ms) Abuki, Baym, Yamamoto and T.H.,arXiv: 1003.0408 [hep-ph]

Spectral continuity at finite μ　　

SB CSC

QGPCP induced by Higgs

CP induced by anomaly

co

nden

sate

s 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 BCS

diquark BEC

UCA/QCD correspondenceUCA/QCD correspondence

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

Neutron matter

quarkMatter?

b fσ

s-wave boson-fermion

scattering length

+0

-0

strong

weak

0weak

strong

0

Maeda, Baym and Hatsuda, Phys. Rev. Lett. 103 (2009) 085301Atomic BF mixtureAtomic BF mixture

Induced superfluidity of composite fermions -- a novel analogy between cold atoms and QCD --

Induced superfluidity of composite fermions -- a novel analogy between cold atoms and QCD --

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

CompositeFermion

cold atoms dense QCD

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

Phase structure and symmetryPhase structure and symmetry

N-BCS b-BEC

Broken and residual symmetries (continuous symmetries)

broken

residual

b,f normal gas

N normal gas b-BEC

N-BCS

0

T

strong couplingstrong coupling weak couplingweak coupling

b,f normal gas

//( )b f1 31 n a

The Hamiltonian density has symmetry.

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

1.1. QCD phase structureQCD phase structure ・ Three major phases in QCD: χSB, QGP and CSC ・ Axial anomaly plays crucial roles everywhere ・ Close similarity with high Tc supercond. & multi-comp. cold atoms

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

・ Continuity of χSB phase and CSC phase

3.3. Spectral continuity in high density QCDSpectral continuity in high density QCD・ Pions are pions.

・ Vector mesons are gluons.

4. Future4. Future・ Real location of the new critical point ? ・ How to detect critical lines and points in lab. experiment ?

・ Tabletop simulations of high density QCD using cold atoms ?

Summary and FutureSummary and Future