# Axial Anomaly, Mismatched Fermi Surfaces and Vector ...

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Axial Anomaly, Mismatched Fermi Surfaces and Vector Interaction in

Dense Neutral Quark Matter

Teiji Kunihiro (Kyoto)

Dense strange nuclei and compressed baryonic matter,Mini symposium, YITP, April 21, 2011

In collaboration with Zhao Zhang

Di-quark fluctuation effects

Conjectured QCD phase diagram Conjectured QCD phase diagram

TT

μμ

Critical pointTc

2Tc

Chiral fluctuation effects

?

TCP

0 0qm =Phase diagram in NJL modelPhase diagram in NJL model

T

CP

TCP

μm

0 5.5qm = MeV

CP

crossover

Asakawa,Yazaki,(1989)

Caution!

Effects of GV on Chiral Restoration

Chiral restoration is shifted to higher densities.The phase transition is weakened.

As GV is increased, First OrderCross Over

GV→Large

Asakawa,Yazaki ’89 /Klimt,Luts,&Weise ’90 / Buballa,Oertel ’96

What would happen when the CSC joins the game?

Importance of Vector-type Interaction

Instanton-anti-instanton molecule model Shaefer,Shuryak (‘98)

[ ] [ ] 82

52

22

52

2 )()(2

1)()(2 LN

iN

GL aa

C

aa

C

+⎭⎬⎫

+−⎩⎨⎧

+= ψγγτψψγτψψγτψψτψ μμ

Renormalization-group analysis N.Evans et al. (‘99)

{ }2200 )()( LLLLllLL GL ψγψψγψ μ−=

Vector interaction naturally appears in the effective theories.

4/1/ =SV GG

( )2

VG μψγ ψ− density-density correlation

( )2 20 0 2V V VG G Gψγ ψ ψγ ψ ρ− → − = − 0ρ ψγ ψ=

Chiral restoration is punished by the vector interaction!

35.0/ =SV GG Another end point appears from lower temperature, and hence there can exist two end points in some range of GV !

(4)

With color superconductivity transition incorporated:Two critical end point! M. Kitazawa, T. Koide, Y. Nemoto and T.K., PTP (’02)

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

Contour of ω withGV /GS =0.35

5MeV

12MeV

15MeV

T=22MeV

μ

M. Kitazawa, et al (’02)

Very shallow or softfor creating diquark-chiral condensation!

EEffect of electric chemical potential with neutral CSCffect of electric chemical potential with neutral CSC

Asymmetric homogenous CSC with charge neutrality

nd > nu > ns Mismatch cooper paring

Mismatch paring or pair breaking, real case

, Fm pδμ δ δ→

Standard BSC paring , rare cace

For two flavor asymmetric homogenous CSC

Abnormal thermal behavior of diquark gapChromomagnetic instibility, imaginary meissner mass

Abnormal thermal behavior of diquark energy gap

( )n p

p

Smearing by T induces the pairing!

Double effects of T : Melting the condensateMore and more components

take part in cooper pairing

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

1Fp 2Fp

( )TΔ

ud

Effects of Charge neutrality on QCD phase diagramEffects of Charge neutrality on QCD phase diagram

•• QCD phase diagram with chiral and CSC transitions with charge QCD phase diagram with chiral and CSC transitions with charge neutralityneutrality

•• Pairing with mismatched Fermi surfacePairing with mismatched Fermi surface•• Competition between chiral and CSCCompetition between chiral and CSC•• Charge neutrality play a role similar to the vectorCharge neutrality play a role similar to the vector--vector(densityvector(density--density) density)

interactin and leads to proliferation of critical points.interactin and leads to proliferation of critical points.

Z. Zhang, K. Fukushima, T.K., PRD79, 014004 (2009)

Combined effect of Vector Interaction and Charge Neutrality constraint

Z. Zhang and T. K., Phys.Rev.D80:014015,2009.;

for 2+1 flavors

chiral

di-quark

vector

anomaly

Kobayashi-Maskawa(’70); ‘t Hooft (’76)

Fierts tr.diquark-chiraldensity coupl.

Model set 2 : M(p=0)= 367.5 MeV , Gd/Gs =0.75

Increasing Gv/Gs

4 types of critical point structure Order of critical-point number : 1, 2, 4, 2,0

4 criticalpoints !

Z. Zhang and T. K., PRD80(2009)

2-flavor case

2+1 flavor case

140MeVs

m =,5.5MeV

u dm =

Z. Zhang and T. K., Phys.Rev.D80:014015,2009.;

Similar to the two-flavor case,with multiple critical points.

the anomaly -induced new CP in the low T region

a la Hatsuda-Tachibana-Yamamoto-Baym (2006)

Incorporating an anomaly term inducing the chiral and diquark mixing

(A) Flavor-symmetric case:Abuki et al, PRD81 (2010),125010

(A’) Role of 2SC in 3-flavor quark matterH. 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 neutralitynor vector interaction.

The role of the anomaly term and G_v under charge-neutrality constraint

Z. Zhang and T.K., arXiv:1102.3263 [hep-ph]

G_V=0:

due to theMismatchedFermi surface

Otherwise,consistentwith Basler-Buballa

Effect of mismatched Fermi sphere

Owing to the mismatched Fermi sphere inherent in the charge-neutralityconstrained system, the pairing gap is induced by the smearing of Fermisurface at moderated temperature!

1st crossover 1st

Effects of G_v

A crossover Region gets to appear, which starts from zeroT.

G_V makes the ph.tr. a crossover at intermediate Twith much smaller K’.

This crossover region is extended to higher temperature region.

Eventually, the ph. tr becomescrossover in thewhole T region.

G_V varied with K’ /K fixed at 1

1. Effects of mismatched Fermi sphere bycharge-neutrality

2. Then effect of G_Vcomes in to make ph. tr. at low Tcross over.

Fate of chromomagnetic instability

G_v=0Finite G_V

4. Summary and concluding remarks4. Summary and concluding remarks4. Summary and concluding remarks

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.

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 goodchance to see large fluctuations of various observables like chiral-diquark-density mixed fluctuations,

+ + † .c

aq q bqq cq q

QCD phase diagram with vector interaction and axial anomalyterms under charge neutrality and beta-equilibrium constraints.

Back Ups

Effects of the vector interaction on the effective chemical potentials

The vector interaction tends to suppress the mismatch of the Fermi spheres of theCooper pairs.

Suppression of the Chromomagnetic instability!

Suppression of the Chromomagnetic instabilitydue to the vector interaction!

Z. Zhang and T. K., Phys.Rev.D80:014015,2009.;

(Partial) resolution of the chromomagnetic instability problem!

Intuitive understanding of the effect of vector interaction on chiral restoration

Kitazawa, Koide, Kunihiro & Nemoto (’02)

Contour maps of thermal potential The possible largedensity leading toCSC is `blamed’by the vector interaction.

Δ Δ

qq qq0Vg = 0Vg ≠