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
Hadron

quark continuity
induced by the axial anomaly
in dense QCD
Introduction
T
m
B
Quark

Gluon Plasma
Color
superconductivity
Hadrons
1st
Critical point
Asakawa &
Yazaki, ’89
Standard picture
Introduction
T
m
B
Quark

Gluon Plasma
Color
superconductivity
Hadrons
1st
?
hadron

quark continuity?
(conjecture)
Schäfer & Wilczek, ’99
Critical point
Asakawa &
Yazaki, ’89
Introduction
T
m
B
Color
superconductivity
Hadrons
New critical point
Yamamoto et al. ’06
What is the origin?
Quark

Gluon Plasma
1st
Critical point
Asakawa &
Yazaki, ’89
・
Symmetry of the system
・
Order parameter
Φ
•
Symmetry:
•
Order parameters :
1.
φ
4
theory in Ising spin system
2.
O(4)
theory in QCD at T
≠
0
Pisarski & Wilczek ’84
What about QCD at T
≠
0 and μ
≠
0
?
Topological structure
of the phase diagram
Interplay
Ginzburg

Landau (GL)
model

independent
approach
e.g.
Axial anomaly
Most general Ginzburg

Landau potential
Instanton effects
＝
Axial anomaly
（
breaking
U(1)
A
）
η’
mass
New critical point
Massless 3

flavor case
Possible
condensates
＝
Axial anomaly
（
breaking
U(1)
A
）
,
: 1
st
order
: 2
nd
order
Phase
diagram
with realistic quark masses
Z
2
phase
Phase
diagram
with realistic quark masses
New critical point
A realization of hadron

quark continuity
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?
Back up slides
Crossover in terms of QCD symmetries
G
V
d
d
V
e
d
d
V
d
d
V
e
d
d
V
V
e
R
L
R
R
i
L
R
R
R
L
L
i
R
L
R
L
i
A
A
A
under
,
6
4
2
†
†
†
†
†
†
†
COE phase : Z
2
CSC phase : Z
4
γ

term : Z
6
COE & CSC phases can
’
t be distinguished by symmetry.
→
They can be continuously connected.
COE phase : Z
2
G
= SU(3)
L
×
SU(3)
R
×
U(1)
B
×
U(1)
A
×
SU(3)
C
Hyper nuclear matter
SU(3)
L
×
SU(3)
R
×
U(1)
B
→
SU(3)
L+R
chiral condensate
broken in the H

dibaryon channel
Pseudo

scalar mesons (
π
etc)
vector mesons (
ρ
etc)
baryons
CFL phase
SU(3)
L
×
SU(3)
R
×
SU(3)
C
×
U(1)
B
→
SU(3)
L+R+C
diquak condensate
broken by
d
NG bosons
massive gluons
massive quarks (CFL gap)
Phase
Symmetry
breaking
Pattern
Order
parameter
U(1)
B
Elementary
excitations
Hadron

quark continuity
(Schäfer & Wilczek, 99)
Continuity between
hyper nuclear matter
&
CFL phase
GL approach for chiral & diquark condensates
Chiral cond.
Φ
:
Diquark cond.
d
:
3
3
★
1
1
3
1
3
3
3
＝
Axial anomaly
（
breaking
U(1)
A
to Z
6
）
6

fermion interaction
Realistic QCD phase structure
m
u,d
= 0, m
s
=
∞
(2

flavor limit)
m
u,d,s
= 0 (3

flavor limit)
Critical point
0
≾
m
u,d
<m
s
≪
∞ (realistic quark masses)
New critical point
≿
≿
Asakawa & Yazaki, 89
hadron

quark continuity
Schäfer & Wilczek, 99
Leading mass term
(up to )
Mass spectra for lighter pions
Generalized GOR relation including σ &
d
Pion spectra in intermediate density region
Mesons on the hadron side
Mesons on the CSC side
Interaction term
Axial anomaly
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)
More realistic conditions
•
Finite quark masses
•
β

equilibrium
•
Charge neutrality
•
Thermal gluon fluctuations
•
Inhomogeneity such as FFLO state
•
Quark confinement
Can the new CP survive under the following?
Basic properties
•
Why ?
assumption: ground state
→
parity +
•
The origin of η’ mass
QCD axial anomaly ( Instanton induced interaction)
Phase diagram (3

flavor)
Crossover between CSC & COE phases & New critical point A
γ>0
γ=0
: 1
st
order
: 2
nd
order
Phase diagram (2

flavor)
b
2
1
b
2
1
b>0
b<0
b
a
2
1
,
2
The emergence of the point A
Modification by the
λ

term
The effective free

energy in COE phase
stationary condition
The origin of the new CP in 2

flavor NJL model
Kitazawa, Koide, Kunihiro & Nemoto, 02
& their TP
p
F
p
T
( )
n p
p
F
p
( )
n p
NG
CSC
This effect plays a role similar to the temperature,
and a new critical point appears.
As
G
V
is increased,
COE phase becomes broader.
becomes larger at the boundary between CSC & NG.
→
The Fermi surface becomes obscure.
Coordinates of the characteristic points in the a

α plane
3

flavor
2

flavor
(b>0)
Crossover in terms of the symmetry discussion
homogenious
& isotropic fluid
Typical phase diagram
symmetry
broken
Ising model in Φ
4
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 model
1:Ising spin,
: magnetization
i j i
ij i
i
i
H J S S h S
S
m S
h=0
Z(2) symmetry : m
⇔
－
m
GL free

energy
2 4
( ) ( )
2 4
a T b T
m m
Z(2)
symmetry allows even powers only.
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=T
C
.
→
a(T)=k(T
－
T
c
) k>0, T
c
: critical temperature
unbroken phase (T>T
c
)
broken phase (T<T
c
)
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.
This system shows 2
nd
order phase transition.
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