Phase Diagram of Dense Neutral Quark Matter

with Axial Anomaly and Vector Interaction

Teiji Kunihiro (Kyoto)

New-type of Fermions on the Lattice 2012/02/09 --- 2012/02/24 YITP, Kyoto University

In collaboration with M. Kitazawa, T. Koide, Y. Nemoto K. Fukushima and Zhao Zhang

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

the softening of 　 the withincreasing T

T

TFluctuations of chiral order parameter around Tc in Lattice QCD

Di-quark fluctuation effects

Conjectured QCD phase diagram Conjectured QCD phase diagram

TT

Critical pointTc

2Tc

Chiral fluctuationeffects

?

What are physics contents, hadrons, partons, or percolated multi-quark states ?

TCP

0 0qm (Tri-)Critical Point in NJL model(Tri-)Critical Point in NJL model

T

CP

TCP

m

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 for CSC

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

82

52

22

52

2)()(

2

1)()(

2L

Ni

NGL aa

C

aa

C

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

2200 )()( LLLLllLL GL

Vector interaction naturally appears in the effective theories.

4/1/ SV GG

2

VG density-density correlation

2 20 0 2V V VG G G 0

M

E

0 m

An important observation is that chiral restoration is suppressed by the vector interaction or density-density interaction!

0 0

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.

qq qq0Vg 0Vg

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

Yet　another　critical　point,　due　to　charge　neutrality.

1st order

G; chiral, H; diquark

“suviver’’ of the 1st-order chiral transition

“remnant’’of the 1st-orderChiral transition

Charge neutrality gives rise to a mismutch of the Fermi surfaces.

At low(moderate) T,diquark-pairing is suppressed(enhanced).

Large diquark-

pairing

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

Effect of electric chemical potential with neutral CSCEffect of electric chemical potential with neutral CSC

Asymmetric homogenous CSC with charge neutrality

nd > nu > nsMismatch cooper paring

Mismatch　paring　　or　pair　breaking,　real　case　

, Fm p

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

( )T

u

d

Yet　another　critical　point,　due　to　charge　neutrality.

1st order

G; chiral, H; diquark

“suviver’’ of the 1st-order chiral transition

“remnant’’of the 1st-orderChiral transition

Charge neutrality gives rise to a mismutch of the Fermi surfaces.

At low(moderate) T,diquark-pairing is suppressed(enhanced).

Large diquark-

pairing

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

Effects of Charge neutrality constraint on the phase diagramEffects of Charge neutrality constraint on the 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 vector-vector(density-density) Charge neutrality play a role similar to the vector-vector(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 critical points !

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

2-flavor case

2+1 flavor case

140MeVsm , 5. 5MeVu 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

G_V=0:

due to theMismatchedFermi surface

Otherwise,consistentwith Basler- Buballa

Z.Zhang, T.K, Phys. Rev. D83 (2011) 114003.

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

Z.Zhang, T.K, (2011)

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.

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

G_v=0Finite G_V

Z.Zhang, T.K, Phys. Rev. D83 (2011) 114003.

The essence of 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

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 remarks4. 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.

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,

† .caq q bqq cq q

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

4. Various possibilities at finite rho:

G_D dependence without g_V

•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.

H .Abuki and T.K. :Nucl. Phys. A, 768 (2006),118

S.Carignano, D. Nickel and M. Buballa, arXiv:1007.1397

( ) ( ( ) ( ))sM S iP x m 2G x 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.

T

QGP

QCD 　 CP

Meson condensations?

?

Precursory hadronicexcitations?

0

CFL

Conjectured QCD phase diagram

H-dibaryon matter?

A few types ofsuperfluidity

CSC

Hadron phase

Liq.-Gas

~150MeV

１ st

Back Ups

Contour of with GV/GS=0.35

5MeV

12MeV

15MeV

T=22MeV

M. Kitazawa, et al (’02)

Very shallow or softfor creating diquark-chiral condensation!

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!