Naoki Yamamoto Univ' of Tokyo

1
Hadron-quark continuity induced by the axial
anomaly in dense QCD

• Naoki Yamamoto (Univ. of Tokyo)
• Tetsuo Hatsuda (Univ. of Tokyo)
• Motoi Tachibana (Saga Univ.)
• Gordon Baym (Univ. of Illinois)

Phys. Rev. Lett. 97 (2006)122001 (hep-ph/0605018
)
Quark Matter 2006 Nov. 15. 2006
2
Introduction
T
Quark-Gluon Plasma
1st
Color superconductivity
Hadrons
mB
Standard picture
3
Introduction
T
Quark-Gluon Plasma
1st
Color superconductivity
?
Hadrons
mB
hadron-quark continuity? (conjecture)
Schäfer Wilczek, 99
4
Introduction
T
Quark-Gluon Plasma
1st
Color superconductivity
Hadrons
mB
New critical point
Yamamoto et al. 06
What is the origin?
5

Ginzburg-Landau (GL) model-independent approach
Symmetry of the system Order parameter F
Topological structure of the phase diagram
e.g.

• f4 theory in Ising spin system
• O(4) theory in QCD at T?0 Pisarski
  Wilczek 84

What about QCD at T?0 and µ?0 ?

• Symmetry
• Order parameters

6
Most general Ginzburg-Landau potential
? mass
New critical point
Instanton effects
7
Massless 3-flavor case
Possible condensates
8
Phase diagram with realistic quark masses
9
Phase diagram with realistic quark masses
New critical point
Z2 phase
A realization of hadron-quark continuity
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Summary Outlook

• 1. Interplay between and
• in model-independent Ginzburg-Landau
  approach
• 2. We found a new critical point at low T
• 3. Hadron-quark continuity in the QCD ground
  state
• 4. QCD axial anomaly plays a key role
• 5. Exicitation spectra?
• at low density and at
  high density
• are continuously connected.
• 6. Future problems
• Real location of the new critical point in T-µ
  plane?
• How to observe it in experiments?

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Back up slides
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Crossover in terms of QCD symmetries
COE phase Z2
CSC phase Z4
?-term Z6
COE CSC phases cant be distinguished by
symmetry. ? They can be continuously connected.
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• Hadron-quark continuity (Schäfer Wilczek, 99)

Continuity between hyper nuclear matter CFL
phase
Hyper nuclear matter SU(3)LSU(3)RU(1)B ? SU(3)
LR chiral condensate broken in the H-dibaryon
channel Pseudo-scalar mesons (p etc) vector
mesons (? etc) baryons
CFL phase SU(3)LSU(3)RSU(3)CU(1)B ?
SU(3)LRC diquak condensate broken by d NG
bosons massive gluons massive quarks (CFL gap)
Phase Symmetry breaking Pattern Order
parameter U(1)B Elementary excitations
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GL approach for chiral diquark condensates
Chiral cond. F Diquark cond. d
Axial anomaly(breaking U(1)A to Z6)

6-fermion interaction
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Realistic QCD phase structure
mu,d 0, ms8 (2-flavor limit)
mu,d,s 0 (3-flavor limit)
?
?
0 ? mu,dltms8 (realistic quark masses)
Critical point
Asakawa Yazaki, 89
New critical point
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Pion spectra in intermediate density region
Mesons on the hadron side
Mesons on the CSC side
Interaction term
Mass spectra for lighter pions
Generalized GOR relation including s d
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Apparent discrepancies of hadron-quark
continuity

• On the CSC side,
• extra massless singlet scalar
• (due to the spontaneous U(1)B breaking)
• 8 rather than 9 vector mesons (no singlet)
• 9 rather than 8 baryons (extra singlet)

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More realistic conditions
Can the new CP survive under the following?

• Finite quark masses
• ß-equilibrium
• Charge neutrality
• Thermal gluon fluctuations
• Inhomogeneity such as FFLO state
• Quark confinement

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Basic properties

• Why ?
• assumption ground state ? parity
• The origin of ? mass
• QCD axial anomaly ( Instanton induced
  interaction)

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Phase diagram (3-flavor)
?0
Crossover between CSC COE phases New critical
point A
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Phase diagram (2-flavor)
bgt0
blt0
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The emergence of the point A
The effective free-energy in COE phase
stationary condition
Modification by the ?-term
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The origin of the new CP in 2-flavor NJL model
Kitazawa, Koide, Kunihiro Nemoto, 02 their TP
As GV is increased,
p
pF
NG
CSC
COE phase becomes broader.
p
pF
D becomes larger at the boundary between CSC
NG. ?The Fermi surface becomes obscure.
This effect plays a role similar to the
temperature, and a new critical point appears.
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Coordinates of the characteristic points in the
a-a plane
3-flavor
2-flavor (bgt0)
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Crossover in terms of the symmetry discussion
homogenious isotropic fluid
symmetry broken
Typical phase diagram
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Ising model in F4 theory

• Model-independent approach based only on the
  symmetry.
• Free-energy is expanded in terms of the order
  parameter F (such as the magnetization) near the
  phase boundary.

Ising model
h0 Z(2) symmetry m ?-m
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GL free-energy
Z(2) symmetry allows even powers only.

• This shows a minimal theory of the system.
• b(T)gt0 is necessary for the stability of the
  system.
• a(T) changes sign at TTC. ? a(T)k(T-Tc) kgt0,
  Tc critical temperature

Whole discussion is only based on the symmetry of
the system. (independent of the microscopic
details of the model)
GL approach is a powerful and general method to
study the critical phenomena.