Phase Diagram of Dense Neutral Quark Matter with

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 2 Tc Tc Chiral fluctuation effects What are physics contents, hadrons, partons, or percolated multi-quark states ? Critical point ? Di-quark fluctuation effects m

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

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.

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 G !

Similarity of the effect of temperature and pairing gap on the chiral condensate. M. Kitazawa et al. PTP, 110 (2003), 185: ar. Xiv: hep-ph/0307278 T Δ

Yet another critical point, due to charge neutrality. Z. Zhang, K. Fukushima, T. K. , PRD 79, 014004 (2009) G; chiral, H; diquark “remnant’’ of the 1 st-order Chiral transition Large diquarkpairing 1 st order “suviver’’ of the 1 st-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 > n u > n s Standard BSC paring , rare cace Mismatch cooper paring Mismatch paring or pair breaking, real case For two flavor asymmetric homogenous CSC Ø Abnormal thermal behavior of diquark gap ØChromomagnetic instibility, imaginary meissner mass

Abnormal thermal behavior of diquark energy gap Smearing by T induces the pairing! d u p Double effects of T : ØMelting the condensate ØMore 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

Yet another critical point, due to charge neutrality. Z. Zhang, K. Fukushima, T. K. , PRD 79, 014004 (2009) G; chiral, H; diquark “remnant’’ of the 1 st-order Chiral transition Large diquarkpairing 1 st order “suviver’’ of the 1 st-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. , PRD 79, 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. D 80: 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 Me. V , Gd/Gs =0. 75 2 -flavor case Z. Zhang and T. K. , PRD 80 (2009) 4 critical points ! Increasing 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. D 80: 014015, 2009. ; 2+1 flavor case 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, PRD 81 (2010), 125010 the anomaly -induced new CP in the low T region

(A’) Role of 2 SC 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. D 83 (2011) 114003. G_V=0: due to the Mismatched Fermi surface Otherwise, consistent with Basler. Buballa

Effect of mismatched Fermi sphere 1 st crossover Z. Zhang, T. K, (2011) 1 st 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. D 83 (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. D 83 (2011) 114003.

Fate of chromomagnetic instability Z. Zhang, T. K, Phys. Rev. D 83 (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 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, 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　2 SC or g 2 SC. • 　The phase structure involving chiral transition at low density region may be parameter dependent and altered.

S. Carignano, D. Nickel and M. Buballa, ar. Xiv: 1007. 1397 E. Nakano and T. Tatsumi, PRD 71 (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? ~150 Me. V QCD　CP １ st 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= 22 Me. V M. Kitazawa, et al (’ 02) 15 Me. V 12 Me. V Very shallow or soft for creating diquark-chiral condensation! 5 Me. V 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. D 80: 014015, 2009. ; (Partial) resolution of the chromomagnetic instability problem!