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 Effects of the vector interaction on phase diagram with color superconductivity Effects of charge and beta-equilibrium constraints Role of Axial anomaly on phase diagram with CSC Summary and concluding remarks

Fluctuations of chiral order parameter around Tc in Lattice QCD   the softening of　the  with increasing T

Conjectured QCD phase diagram Chiral fluctuation effects 2Tc What are physics contents, hadrons, partons, or percolated multi-quark states ? QGP Tc Critical point Di-quark fluctuation effects ? Hadron CSC m

(Tri-)Critical Point in NJL model MeV CP crossover TCP T Asakawa,Yazaki,(1989) CP TCP 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 Instanton-anti-instanton molecule model Shaefer,Shuryak (‘98) Renormalization-group analysis N.Evans et al. (‘99) Vector interaction naturally appears in the effective theories. m density-density correlation An important observation is that chiral restoration is suppressed by the vector interaction or density-density interaction!

Contour maps of thermal potential 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.

(4) 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 !

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 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.

Effect of electric chemical potential with neutral CSC Asymmetric homogenous CSC with charge neutrality Mismatch cooper paring nd > nu > 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

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

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.

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 for 2+1 flavors diquark-chiral density coupl. Fierts tr. Kobayashi-Maskawa(’70); ‘t Hooft (’76)

Increasing Gv/Gs Model set 2 : M(p=0)= 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

2+1 flavor case 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 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 Basler- Buballa

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!

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. Finite G_V G_v=0

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

Philippe de Forcrand and Owe Philipesen (‘08) 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. 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:

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 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 CFL  QGP １st T Precursory hadronic excitations? QGP ~150MeV QCD　CP １st Hadron phase ? CSC Liq.-Gas CFL m  H-dibaryon matter? A few types of superfluidity Meson condensations?

Back Ups

m Contour of w with GV/GS=0.35 T= 22MeV 15MeV 12MeV 5MeV 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!