Phase Diagram of Dense Neutral Quark Matter with Axial Anomaly and Vector Interaction

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Phase Diagram of Dense Neutral Quark
Matterwith 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
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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

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Fluctuations of chiral order parameter
around Tc in Lattice QCD
T
T
m
?
?
the softening of the ? with increasing T
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(No Transcript)
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Conjectured QCD phase diagram

T
Chiral fluctuationeffects
2Tc
What are physics contents, hadrons, partons, or
percolated multi-quark states ?
QGP
Tc
Di-quark fluctuation effects
Critical point
?
Hadron
CSC
m
6
(Tri-)Critical Point in NJL model
TCP
T
Asakawa,Yazaki,(1989)
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Caution!
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Effects of GV on Chiral Restoration
GV?Large
First Order
As GV is increased,
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?
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Importance of Vector-type Interaction for CSC
An important observation is that chiral
restoration is suppressed by the vector
interaction or density-density interaction!
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Intuitive understanding of the effect of
vector interaction on chiral restoration
Kitazawa, Koide, Kunihiro Nemoto (02)
Contour maps of thermal potential
The possible large density leading to CSC is
blamed by the vector interaction.
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With color superconductivity transition
incorporated Two critical end point!
M. Kitazawa, T. Koide, Y. Nemoto and T.K., PTP
(02)
(4)
Another end point appears from lower
temperature, and hence there can exist two end
points in some range of GV !
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Similarity of the effect of temperature and
pairing gap on the chiral condensate.
M. Kitazawa et al. PTP, 110 (2003),
185 arXivhep-ph/0307278
T
?
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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
1st order
Large diquark- pairing
suviver of the 1st-order chiral transition
At low(moderate) T, diquark-pairing is
suppressed(enhanced).
Charge neutrality gives rise to a mismutch of
the Fermi surfaces.
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• Effect of electric chemical potential with
  neutral CSC

Asymmetric homogenous CSC with charge neutrality
Mismatch cooper paring
nd gt nu gt ns
Mismatch paring or pair breaking, real case
Standard BSC paring , rare cace
For two flavor asymmetric homogenous CSC

• Abnormal thermal behavior of diquark gap
• Chromomagnetic instibility, imaginary meissner
  mass

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Abnormal thermal behavior of diquark energy gap
Smearing by T induces the pairing!
d
u
p

• Melting the condensate
• More and more components take part in cooper
  pairing

Double effects of T
Competition between these two effects gives rise
to abormal thermal behavior of diquark
condensate
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
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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
1st order
Large diquark- pairing
suviver of the 1st-order chiral transition
At low(moderate) T, diquark-pairing is
suppressed(enhanced).
Charge neutrality gives rise to a mismutch of
the Fermi surfaces.
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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.

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Combined effect of Vector Interaction and Charge
Neutrality constraint
Z. Zhang and T. K., Phys.Rev.D80014015,2009.
chiral
di-quark
vector
anomaly
for 21 flavors
Fierts tr.
diquark-chiral density coupl.
Kobayashi-Maskawa(70) t Hooft (76)
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Model set 2 M(p0) 367.5 MeV , Gd/Gs
0.75
2-flavor case
Z. Zhang and T. K., PRD80 (2009)
Increasing Gv/Gs
4 critical points !
4 types of critical point structure Order of
critical-point number 1, 2, 4, 2,0
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Z. Zhang and T. K., Phys.Rev.D80014015,2009.
21 flavor case
Similar to the two-flavor case, with multiple
critical points.
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the anomaly-induced new CP in the low T region

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
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(A) Role of 2SC in 3-flavor quark matter
H. Basler and M. Buballa, PRD 82 (2010),094004
with
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(B) Realistic case with massive strange quark
ltlt
H. Basler and M. Buballa, (2010)
Notice! Without charge neutrality nor vector
interaction.
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The role of the anomaly term and G_v under
charge-neutrality constraint
Z.Zhang, T.K, Phys. Rev. D83 (2011) 114003.
G_V0
due to the Mismatched Fermi surface
Otherwise, consistent with Basler- Buballa
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Effect of mismatched Fermi sphere
Z.Zhang, T.K, (2011)
1st
crossover
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!
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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.
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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.
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Fate of chromomagnetic instability
Z.Zhang, T.K, Phys. Rev. D83 (2011) 114003.
Finite G_V
G_v0
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The essence of Effects of GV on Chiral
Restoration
GV?Large
First Order
As GV is increased,
Cross Over
Chiral restoration is shifted to higher
densities. The phase transition is weakened.
Asakawa,Yazaki 89 /Klimt,Luts,Weise 90 /
Buballa,Oertel 96
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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)
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4. Summary and concluding remarks
QCD phase diagram with vector interaction and
axial anomaly terms under charge neutrality and
beta-equilibrium constraints.

• 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,

4. Various possibilities at finite rho
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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.

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S.Carignano, D. Nickel and M. Buballa,
arXiv1007.1397
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.
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Conjectured QCD phase diagram
T
QGP
Precursory hadronic excitations?
150MeV
QCD CP
1st
Hadron phase
?
CSC
Liq.-Gas
CFL
m
?
0
H-dibaryon matter?
A few types of superfluidity
Meson condensations?
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Back Ups
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Contour of w with GV/GS0.35
T 22MeV
M. Kitazawa, et al (02)
15MeV
12MeV
Very shallow or soft for creating diquark-chiral
condensation!
5MeV
m
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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!
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Suppression of the Chromomagnetic instability due
to the vector interaction!
Z. Zhang and T. K., Phys.Rev.D80014015,2009.
(Partial) resolution of the chromomagnetic
instability problem!