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.