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

kitefleaUrban and Civil

Nov 15, 2013 (3 years and 6 months ago)

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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.