Transcript ppt - KIAA
Kazuya Nishiyama Kyoto University Collaborator: Toshitaka Tatsumi, Shintaro Karasawa, Ryo Yoshiike Quarks and Compact Stars 2014 October 2014, PKU, Beijing T ΞΌ Usually, The QCD phase structure is studied by assuming that the order parameter is temporally and spatially constant. Is it possible that Non-uniform phase appears in QCD phase diagram? β’ Inhomogeneous phase appears in QCD γ»Order parameter Ξ(π§) = ππ + π πππΎ 5 π 3 π β Typical configurations. γ»Dual Chiral Density Wave(DCDW) Phase is inhomogeneous ΞDCDW π§ = π eπππ§ E.Nakano, T.Tatsumi (2005) D.Nickel (2009) G.Basar(2008) β¦β¦. γ»Phase Diagram Restored RKC γ»Real kink Crystal(RKC) Amplitude is inhomogeneous 2π π 2ππ§ βRKC π§ = sn ;π 1+ π 1+ π Inhomogeneous phase appears in intermediate ΞΌ β’ Quarks and Hadrons in Strong magnetic field β’ Magnetar ο½1015 Gauss β’ Heavy Ion Collision ο½1017 Gauss β’ Early Universe Much higher β’ Magnetic field causes various phenomena β’ β’ β’ β’ et. al.(1994) Magnetic Catalysis, Magnetic Inhibition V.P.Gusynin, G.S.Bali, et, al. (2011) K.Fukushima, et. al (2008) Chiral magnetic effect Charged vector meson condensation β¦. QCD phase structure must be changed by taking account to both of Inhomogeneity and magnetic field. β’ DCDW in the external magnetic field I. E. Frolov,et.al. Rev. D 82, 076002 (2010) ΞDCDW π§ = π eπππ§ ΞΌ=0.3 q/2 A: Restored phase B,C,D: DCDW phase βDCDW grows by magnetic field However, RKC is more favorable than DCDW without magnetic field β’ Purpose of the current study β’ What inhomogeneous phase is favored in magnetic field β’ How mechanism of growth of DCDW in magnetic field β’ Model Mean field NJL model in the external magnetic field. πΏ = πππ·π πΎ π π + 2πΊ ππ ππ + πππΎ 5 π π π πππΎ5 π π π β πΊ[ ππ 2 Ξ(π§) = β2πΊ[ ππ + π πππΎ 5 π 3 π ] We assume that magnetic field is parallel to modulation of order parameters. β’ Hybrid Configuration More general type condensate which includes DCDW and RKC Ξ π§ β M π§ π πππ§ = 2π π 2ππ§ sn ; π × π πππ§ 1+ π 1+ π DCDW RKC π β1 ΞDCDW (π§) Ξ π§ This configuration is characterized by q,Ξ½,m 2 + πππΎ 5 π π π ] qβ0 βRKC π§ β’ 1 particle Energy Spectrum Eπ,π,πΌ = πΉπΌ + π Eπ=0,πΌ π 2 π = πΉπΌ + 2 2π ππ π΅ π πΉπΌ + π 2 1+ 2 n=1,2,β¦.. π = ±1 ο½οΌLandau levels (n=0,1,2β¦) πΉπΌ οΌ1+1dim RKC Energy spectrum n=0 n=0, Energy spectrum is asymmetric. β’ Free energy Ξ(π§) Ξ©= 4πΊ 2 1 β ππ π½ π ππ π΅ 2π β ππΉ π πΉ ln 1 + π βπ½ Eπππ (πΌ)βπ π π=0 πΞ© Phase structure is determined by Stationary conditions ππ = πΞ© = πΞ© =0 ππ ππ T.Tatsumi, K.N, S.Karasawa arXiv:1405.2155 β’ Quark Density at T=0 πΞ© β = ππ ππ π ππ π΅ 2π β ππΉ π πΉ π(EπππΉ )π(π β EπππΉ ) π π=0 +ππ π 1 ππ π΅ 2 2π E sgn(Eπ=0,πΉ ) πΉ Anomalous Quark Number Density by Spectral Asymmetry ΞΌ q/2+m A.J.Niemi (1985) For DCDW (m>q/2) πππππ = ππ π 1 ππ π΅ π 2 2π π 0 q/2-m Ξ©ππππ β ππ΅ππ This term is first order of q βq=0 is not minimum point βInhomogeneous phase is more favorable than homogeneous broken phase. β’ Phase Diagram at T=0 A: Weak DCDW phase B: Hybrid C: Strong DCDW phase D Restored ππ΅[MeV] C A B D π[MeV] B=0, the order parameter is real. Homogeneous phase and RKC phase appear. Weak B, the order parameter is complex but q is small Strong B, DCDW is favored everywhere. (a) π΅ = 0 (b) ππ΅ = 70MeV (ο½5×1016 Gauss) β β2 β k β q/2 Homo. Broken RKC 1/2 β β2 β k β q/2 DCDW Restored 1/2 DCDW Restored π[MeV] π[MeV] k is wavenumber of amplitude modulation π = 2 1 + π K(π)/π (b) ππ΅ = 120MeV (ο½1.4×1017 Gauss) β β2 β k β q/2 (c) DCDW (b) (a) DCDW π[MeV] 1/2 β’ Summary β’ Hybrid type configuration is used Ξ π§ β M π§ π πππ§ = 2π π 2ππ§ sn ; π × π πππ§ 1+ π 1+ π β’ In magnetic field, DCDW is favored due to Spectral asymmetry β’ Magnetic field causes inhomogeneity of phase β’ Hybrid phase appears in the magnetic field β’ Broken Phase expands by magnetic field β’ Outlook β’ Phase diagram at Tβ 0 β’ Strangeness β’ Isospin chemical potential γ»B=0 case Hamiltonian has Ξ β ββ symmetry Ξ©πΊπΏ = πΌ0 + πΌ2 Ξ 2 + πΌ4 Ξ 4 + Ξβ² 2 +πΌ6 Ξ 6 + 4 Ξ 2 Ξβ² 2 + Im Ξβ²Ξβ πΌ2 = πΌ4 = 0 is Lifshitz point 2 + 12 Ξβ²β² 2 γ»Bβ 0 case Ξ β ββ symmetry is broken. βOdd order term appears β Ξ©πΊπΏ = πΌ0 + πΌ2 Ξ 2 + πΌ3 Im ΞΞβ² + πΌ4 Ξ 4 + Ξβ² +πΌ5 Im Ξβ²β² β 3 Ξ 2 Ξ Ξβ² +πΌ6 Ξ 6 + 4 Ξ 2 B=0 or ΞΌ=0 βOdd term vanishes New Lifshitz point appears at πΌ2 = πΌ3 = 0 Ξβ² 2 β 2 + Im Ξβ²Ξβ 2 + 12 Ξβ²β² 2 π΅=0 Ξ 2 1/2 πΏβ1 π =0 everywhere L: period of amplitude modulation ππ΅ = 80MeV Ξ2 1/2 πΏβ1 β’ Broken phase expands by magnetic field β’ Phase modulation grows near the βCritical Pointβ π Quark Gluon Plasma Hadron Liquid-Gas transition Color Superconductor