Naoki Yamamoto (Univ. of Tokyo)Tetsuo Hatsuda (Univ. of Tokyo)Motoi Tachibana (Saga Univ.)

Gordon Baym (Univ. of Illinois)

Phys. Rev. Lett. Phys. Rev. Lett. 97 (2006)12200197 (2006)122001

(hep-ph/0605018(hep-ph/0605018 ))

Quark Matter 2006 Nov. 15. 2006

Hadron-quark continuity Hadron-quark continuity induced by the axial anomaly induced by the axial anomaly

in dense QCDin dense QCD

IntroductionIntroduction

T

Quark-Gluon PlasmaQuark-Gluon Plasma

Color Color superconductivitysuperconductivityHadronsHadrons

1st1stCritical pointCritical pointAsakawa & Yazaki, ’89

Standard pictureStandard picture

IntroductionIntroduction

T

Quark-Gluon PlasmaQuark-Gluon Plasma

Color Color superconductivitysuperconductivityHadronsHadrons

1st1st

?

hadron-quark continuity?hadron-quark continuity? (conjecture)(conjecture) Schäfer & Wilczek, ’9

9

Critical pointCritical pointAsakawa & Yazaki, ’89

IntroductionIntroduction

T

Color Color superconductivitysuperconductivityHadronsHadrons

New critical New critical pointpoint

Yamamoto et al. ’06

What is the What is the origin?origin?

Quark-Gluon PlasmaQuark-Gluon Plasma

1st1stCritical pointCritical pointAsakawa & Yazaki, ’89

・ ・ Symmetry of the systemSymmetry of the system

・ ・ Order parameter Order parameter ΦΦ

• Symmetry:Symmetry:

• Order parameters :Order parameters :

1.1. φφ44 theory in Ising spin system theory in Ising spin system

2.2. O(4)O(4) theory in QCD at Ttheory in QCD at T≠≠0 0 Pisarski & Wilczek ’84

What about QCD at TWhat about QCD at T≠≠0 and μ0 and μ≠≠00 ??

Topological Topological structure of the structure of the phase diagramphase diagram

InterplayInterplay

Ginzburg-Landau (GL) Ginzburg-Landau (GL) model-independentmodel-independent approachapproach

e.ge.g..

Axial Axial anomalyanomaly

Most general Ginzburg-Landau potentialMost general Ginzburg-Landau potential

Instanton effectsInstanton effects＝ Axial Axial anomalyanomaly （（ brebreakingaking U(1)U(1)AA ））

η’η’ mass mass

New critical pointNew critical point

Massless 3-flavor caseMassless 3-flavor case

Possible Possible condensatescondensates

＝ Axial Axial anomalyanomaly （（ brebreakingaking U(1)U(1)AA ））

,

: 1st order: 2nd order

Phase Phase diagramdiagram with realistic quark masses with realistic quark masses

ZZ22 phase phase

Phase Phase diagramdiagram with realistic quark masses with realistic quark masses

New critical New critical pointpoint

A realization of hadron-quark continuityA realization of hadron-quark continuity

Summary & OutlookSummary & Outlook1. Interplay between and 1. Interplay between and in model-independent Ginzburg-Landau approachin model-independent Ginzburg-Landau approach2. We found a new critical point at low T2. We found a new critical point at low T3. Hadron-quark continuity in the QCD ground state3. Hadron-quark continuity in the QCD ground state4. QCD axial anomaly plays a key role4. QCD axial anomaly plays a key role

5. Exicitation spectra?5. Exicitation spectra? at low density and at high density at low density and at high density

are continuously connected. are continuously connected. 6. Future problems6. Future problems

• Real location of the new critical point in T-μ plane?• How to observe it in experiments?

Back up slides

Crossover in terms of QCD symmetriesCrossover in terms of QCD symmetries

GVddVedd

VddVeddVVe

RLRRi

LR

RRLLi

RLRLi

A

AA

under

,6

42

†††

††††

　

　　 　

COE phase : COE phase : ZZ22

CSC phase : CSC phase : ZZ44

γγ-term : Z-term : Z66

COE & CSC phases can’t be distinguished by COE & CSC phases can’t be distinguished by symmetry.symmetry.

→ → They can be continuously connected.They can be continuously connected.

COE phase : ZCOE phase : Z22

G G = SU(3)= SU(3)LL×SU(3)×SU(3)RR×U(1)×U(1)BB×U(1)×U(1)AA×SU(3)×SU(3)CC

Hyper nuclear matterHyper nuclear matter

SU(3)SU(3)LL×SU(3)×SU(3)RR×U(1)×U(1)BB

→ → SU(3)SU(3) L+R L+R

chiral condensatechiral condensate

broken in the H-dibaryon channel broken in the H-dibaryon channel

Pseudo-scalar mesons (Pseudo-scalar mesons (ππ etc) etc)

vector mesons (vector mesons (ρρ etc) etc)

baryonsbaryons

CFL phaseCFL phase

SU(3)SU(3)LL×SU(3)×SU(3)RR×SU(3)×SU(3)CC×U(1)×U(1)BB

→ → SU(3)SU(3)L+R+CL+R+C

diquak condensate diquak condensate

broken by broken by dd

NG bosonsNG bosons

massive gluonsmassive gluons

massive quarks (CFL gap) massive quarks (CFL gap)

PhasePhaseSymmetry Symmetry breaking breaking PatternPattern

Order Order parameterparameter

U(1)U(1)BB

ElementarElementary y

excitations excitations

Hadron-quark continuityHadron-quark continuity (Schäfer & Wilczek, 99)

Continuity between Continuity between hyper nuclear matterhyper nuclear matter & & CFL CFL phasephase

GL approach for chiral & diquark condensatesGL approach for chiral & diquark condensates

Chiral cond.Chiral cond. Φ Φ::

Diquark cond.Diquark cond. d d ::

33 33★★ 11

1133

11

33

3333

＝ Axial Axial anomalyanomaly （（ breakingbreaking U(1)U(1)AA to Zto Z66 ））

6-fermion interaction6-fermion interaction

Realistic QCD phase structureRealistic QCD phase structure

mmu,d u,d = 0, m= 0, mss==∞ ∞ (2-flavor limit)(2-flavor limit)mmu,d,s u,d,s = 0 = 0 (3-flavor limit)(3-flavor limit)

Critical Critical pointpoint

0 0 ≾≾ mmu,du,d<m<mss≪∞ (realistic quark masses)≪∞ (realistic quark masses)

New critical New critical pointpoint

≿≿ ≿≿

Asakawa & Yazaki, 89

hadron-quark continuityhadron-quark continuity Schäfer & Wilczek, 99

Leading mass termLeading mass term (up to )

Mass spectra for lighter pionsMass spectra for lighter pions

Generalized GOR relation including σ Generalized GOR relation including σ & & dd

Pion spectra in intermediate density regionPion spectra in intermediate density regionMesons on the hadron Mesons on the hadron sideside

Mesons on the CSC Mesons on the CSC sideside

Interaction Interaction termterm

Axial anomalyAxial anomaly

Apparent discrepancies Apparent discrepancies of “hadron-quark of “hadron-quark

continuity”continuity”

On the CSC side,On the CSC side,• extra massless singlet scalar extra massless singlet scalar

(due to the spontaneous U(1)(due to the spontaneous U(1)BB breaking) breaking)

• 8 rather than 9 vector mesons (no 8 rather than 9 vector mesons (no singlet)singlet)

• 9 rather than 8 baryons (extra singlet)9 rather than 8 baryons (extra singlet)

More realistic conditions More realistic conditions

• Finite quark massesFinite quark masses• β-equilibrium β-equilibrium • Charge neutralityCharge neutrality• Thermal gluon fluctuationsThermal gluon fluctuations• Inhomogeneity such as FFLO stateInhomogeneity such as FFLO state• Quark confinementQuark confinement

Can the new CP survive under the Can the new CP survive under the following?following?

Basic propertiesBasic properties• Why ?Why ?

assumption: ground state assumption: ground state →→ parity + parity +

• The origin of η’ massThe origin of η’ mass

QCD axial anomaly ( Instanton induced interaction)QCD axial anomaly ( Instanton induced interaction) 　　

Phase diagram (3-flavor)Phase diagram (3-flavor)

Crossover between CSC & COE phases & New critical Crossover between CSC & COE phases & New critical point A point A

γ>0γ=0 : 1st order: 2nd order

Phase diagram (2-flavor)Phase diagram (2-flavor)

b2

1 b

2

1

b>0 b<0

ba2

1 ,2

The emergence of the point AThe emergence of the point A

Modification by the Modification by the λλ-term-term

The effective free-energy in COE The effective free-energy in COE phasephase

stationary condition

The origin of the new CP in 2-flavor NJL modelThe origin of the new CP in 2-flavor NJL modelKitazawa, Koide, Kunihiro & Nemoto, 02

& their TP

pF p

T( )n p

pF p

( )n p

NGNGCSCCSC

This effect plays a role similar to the This effect plays a role similar to the temperature, and a new critical point temperature, and a new critical point appears.appears.

As As GGVV is increased, is increased,

COE phase becomes COE phase becomes broader.broader. becomes larger at the boundary between CSC becomes larger at the boundary between CSC & NG. →The Fermi surface becomes obscure.& NG. →The Fermi surface becomes obscure.

Coordinates of the characteristic points in the a-α planeCoordinates of the characteristic points in the a-α plane

3-3-flavorflavor

2-flavor 2-flavor (b>0)

Crossover in terms of the symmetry Crossover in terms of the symmetry discussiondiscussion

homogenious & isotropic fluid

Typical phase diagram

symmetrybroken

Ising model in ΦIsing model in Φ44 theory theory

• Model-independent approach based only on the symmetry.

• Free-energy is expanded in terms of the order parameter Φ (such as the magnetization) near the phase boundary.Ising modelIsing model

1: Ising spin,

: magnetization

i j iij i

i

i

H J S S h S

S

m S

h=0 Z(2) symmetry : m ⇔ － m

GL free-energyGL free-energy

2 4( ) ( )

2 4

a T b Tm m Z(2) symmetry allows even powers

only.

This shows a minimal theory of the system.This shows a minimal theory of the system.

• b(T)>0 is necessary for the stability of the system.

• a(T) changes sign at T=TC. → a(T)=k(T － Tc) k>0, Tc: critical temperature

unbroken phase (T>Tc) broken phase (T<Tc)

Whole discussion is only based on the symmetry of the Whole discussion is only based on the symmetry of the system. (independent of the microscopic details of the system. (independent of the microscopic details of the

model)model) GL approach is a powerful and general method GL approach is a powerful and general method

to study the critical phenomena.to study the critical phenomena.

This system shows 2This system shows 2ndnd order phase order phase transition.transition.