Transcript Renormalization-group Method Applied to Derivation and

Phase Diagram of Dense Neutral
Quark Matter
with Axial Anomaly and Vector
Interaction
Teiji Kunihiro (Kyoto)
In collaboration with
M. Kitazawa, T. Koide, Y. Nemoto
K. Fukushima and Zhao Zhang
New-type of Fermions on the Lattice
2012/02/09 --- 2012/02/24
YITP, Kyoto University
Contents of talk
1. Effects of the vector interaction on phase
diagram with color superconductivity
2. Effects of charge and beta-equilibrium
constraints
3. Role of Axial anomaly on phase diagram with
CSC
4. Summary and concluding remarks
Fluctuations of chiral order
parameter
around Tc in Lattice QCD
T
T
m


the softening of the  with
increasing T
Conjectured QCD phase diagram
T
Chiral fluctuation
effects
2Tc
Tc
What are physics contents,
hadrons, partons, or percolated multi-quark states ?
Critical point
?
Di-quark
fluctuation effects
m
(Tri-)Critical Point in NJL model
mq0  5.5
mq0  0
MeV
TCP
CP
T
Asakawa,Yazaki,(1989)
TCP
m
CP
m
Caution!
Effects of GV on Chiral Restoration
GV→Large
As GV is increased,
First Order
Cross Over
Chiral restoration is shifted to higher densities.
The phase transition is weakened.
Asakawa,Yazaki ’89 /Klimt,Luts,&Weise ’90 / Buballa,Oertel ’96
What would happen when the CSC joins the game?
Importance of Vector-type Interaction for CSC
Vector interaction naturally appears in the effective theories.
Instanton-anti-instanton molecule model Shaefer,Shuryak (‘98)



  L
 2
1
a m
2
a m
2
L  G  2 ( a ) 2  ( ai 5 ) 2 
(




)

(





)
5
2 NC2
 NC

8
GV / GS  1 / 4
Renormalization-group analysis
L0LL  Gll ( L 0 L )2  ( L m L )2 
GV   
m
2
E
m
density-density correlation
GV  0   GV  0
2
N.Evans et al. (‘99)
2
 GV  2
   0


M
0 m
  0
An important observation is that
chiral restoration is suppressed by the vector interaction
or density-density interaction!
  0
Intuitive understanding of the effect of vector
interaction on chiral restoration
Kitazawa, Koide, Kunihiro & Nemoto (’02)
Contour maps of thermal potential


gV  0
qq
gV  0
qq
The possible large
density leading to
CSC is `blamed’
by the vector
interaction.
With color superconductivity transition incorporated:
Two critical end point! M. Kitazawa, T. Koide, Y. Nemoto and T.K., PTP (’02)
(4)
GV / GS  0.35
Another end point appears from lower temperature,
and hence there can exist two end points in some
range of G !
Similarity of the effect of temperature and pairing gap on
the chiral condensate.
M. Kitazawa et al.
PTP, 110 (2003), 185:
arXiv:hep-ph/0307278
T
Δ
Yet another critical point, due to charge neutrality.
Z. Zhang, K. Fukushima, T.K., PRD79, 014004 (2009)
G; chiral, H; diquark
“remnant’’
of the 1st-order
Chiral transition
Large diquarkpairing
1st order
“suviver’’ of the 1st-order
chiral transition
Charge neutrality gives rise to
a mismutch of the Fermi surfaces.
At low(moderate) T,
diquark-pairing is
suppressed(enhanced).
Effect of electric chemical potential with neutral CSC
Asymmetric homogenous CSC with charge neutrality
nd > nu > ns
Mismatch cooper paring
m,  m   pF
Standard BSC
paring , rare cace
Mismatch paring
or pair breaking,
real case
For two flavor asymmetric homogenous CSC
 Abnormal thermal behavior of diquark gap
Chromomagnetic instibility, imaginary meissner mass
Abnormal thermal behavior of diquark energy gap
Smearing by T induces the pairing!
n( p )
d
u
p1F p2F
Double effects of T :
p
Melting the condensate
More and more components
take part in cooper pairing
Competition between these two effects gives rise to
abormal thermal behavior of diquark condensate
 (T )
Enhancing the competition between chiral
condensate and diquark condensate for
somewhat larger T, leading to a nontrivial
impact on chiral phase transition
Shovkovy and Huang, PLB 564, (2003) 205
Yet another critical point, due to charge neutrality.
Z. Zhang, K. Fukushima, T.K., PRD79, 014004 (2009)
G; chiral, H; diquark
“remnant’’
of the 1st-order
Chiral transition
Large diquarkpairing
1st order
“suviver’’ of the 1st-order
chiral transition
Charge neutrality gives rise to
a mismutch of the Fermi surfaces.
At low(moderate) T,
diquark-pairing is
suppressed(enhanced).
Effects of Charge neutrality constraint on the phase diagram
Z. Zhang, K. Fukushima, T.K., PRD79, 014004 (2009)
• QCD phase diagram with chiral and CSC transitions with charge
neutrality
• Pairing with mismatched Fermi surface
• Competition between chiral and CSC
• Charge neutrality play a role similar to the vector-vector(density-density)
interactin and leads to proliferation of critical points.
Combined effect of Vector Interaction and Charge
Neutrality constraint
Z. Zhang and T. K., Phys.Rev.D80:014015,2009.;
chiral
di-quark
vector
anomaly
diquark-chiral
density coupl.
Fierts tr.
for 2+1 flavors
Kobayashi-Maskawa(’70); ‘t Hooft (’76)
Model set 2 : M(p=0)= 367.5 MeV , Gd/Gs =0.75
2-flavor case
Z. Zhang and
T. K., PRD80
(2009)
Increasing
4 critical
points !
Gv/Gs
4 types of critical point structure
Order of critical-point number : 1, 2, 4, 2,0
Z. Zhang and T. K., Phys.Rev.D80:014015,2009.;
2+1 flavor case
mu,d  5.5MeV ms  140MeV
Similar to the two-flavor case,
with multiple critical points.
Incorporating an anomaly term inducing the chiral and
diquark mixing
a la Hatsuda-Tachibana-Yamamoto-Baym (2006)
(A) Flavor-symmetric case:
Abuki et al, PRD81 (2010),
125010
the anomaly
-induced new CP
in the low T region
(A’) Role of 2SC in 3-flavor quark matter
H. Basler and M. Buballa,
PRD 82 (2010),094004
with
(B) Realistic case with massive strange quark;
<<
H. Basler and M. Buballa,
(2010)
Notice!
Without charge neutrality
nor vector interaction.
The role of the anomaly term and G_v
under charge-neutrality constraint
Z.Zhang, T.K, Phys. Rev. D83 (2011) 114003.
G_V=0:
due to the
Mismatched
Fermi surface
Otherwise,
consistent
with BaslerBuballa
Effect of mismatched Fermi sphere
1st
crossover
Z.Zhang, T.K, (2011)
1st
Owing to the mismatched Fermi sphere inherent in the charge-neutrality
constrained system, the pairing gap is induced by the smearing of Fermi
surface at moderated temperature!
Effects of G_v
G_V makes the ph.tr. a crossover at intermediate T
with much smaller K’.
A crossover
Region gets to
appear, which
starts from zero
T.
Eventually,
the ph. tr becomes
crossover in the
whole T region.
This crossover region is extended to
higher temperature region.
Z.Zhang, T.K, Phys. Rev. D83 (2011) 114003.
G_V varied with K’ /K fixed at 1
1. Effects of mismatched
Fermi sphere by
charge-neutrality
2. Then effect of G_V
comes in to make
ph. tr. at low T
cross over.
Z.Zhang, T.K, Phys. Rev. D83 (2011) 114003.
Fate of chromomagnetic instability
Z.Zhang, T.K, Phys. Rev. D83 (2011) 114003.
G_v=0
Finite G_V
The essence of Effects of GV on Chiral Restoration
GV→Large
As GV is increased,
First Order
Cross Over
Chiral restoration is shifted to higher densities.
The phase transition is weakened.
Asakawa,Yazaki ’89 /Klimt,Luts,&Weise ’90 / Buballa,Oertel ’96
responsible for the disappearance of QCD critical point at low
density according to recent lattice stimulation ?
Philippe de Forcrand and Owe Philipesen (‘08)
GV → Large
K. Fukushima (‘08)
4. Summary and concluding remarks
QCD phase diagram with vector interaction and axial anomaly
terms under charge neutrality and beta-equilibrium constraints.
1. There are still a room of other structure of the QCD phase diagram
with multiple critical points when the color superconductivity and
the vector interaction are incorporated.
G_v is responsible for the appearance of another CP at low T, but not
axial anomaly term in the realistic case.
2. The new anomaly-induced interaction plays the similar role as G_V
under charge- neutrality constraint.
3. The message to be taken in the present MF calculation:
It seems that the QCD matter is very soft along the critical line when
the color superconductivity is incorporated; there can be a good
chance to see large fluctuations of various observables like
chiral-diquark-density mixed fluctuations,
aqcq  bqq  cq q.
†
4. Various possibilities at finite rho:
G_D dependence without g_V
H .Abuki and T.K. :
Nucl. Phys. A, 768 (2006),118
•The phase in the highest temperature is 2SC or g2SC.
• The phase structure involving chiral transition at low density region may
be parameter dependent and altered.
S.Carignano, D. Nickel and M.
Buballa, arXiv:1007.1397
M (x)  m  2Gs (S (x)  iP(x))
E. Nakano and T.Tatsumi, PRD71 (2005)
Interplay between G_V and Polyakov loop is not incorporated;
see also P. Buescher and T.K., Ginzburg-Levanyuk analysys shows also an
existence of Lifschitz point at finite G_V.
Spatial dependence of Polyakov loop should be considered explicitly.
Conjectured QCD phase diagram
T
QGP
Precursory hadronic
excitations?
~150MeV
QCD CP
１st
Hadron phase
Liq.-Gas
0
A few types of
superfluidity
?
CSC
CFL
m
H-dibaryon matter?
Meson condensations?
Back Ups
Contour of w with
GV/GS=0.35
T=
22MeV
M. Kitazawa, et al (’02)
15MeV
12MeV
Very shallow or soft
for creating diquark-chiral
condensation!
5MeV
m
Effects of the vector interaction on
the effective chemical potentials
The vector interaction tends to suppress the mismatch of the Fermi spheres of the
Cooper pairs.
Suppression of the Chromomagnetic instability!
Suppression of the Chromomagnetic instability
due to the vector interaction!
Z. Zhang and T. K., Phys.Rev.D80:014015,2009.;
(Partial) resolution of the chromomagnetic instability problem!