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高密度クォーク物質における カイラル凝縮とカラー超伝導の競合

高密度クォーク物質における カイラル凝縮とカラー超伝導の競合. 国広　悌二 ( 京大基研） 東大特別講義 2005 年 12 月 5-7 日. Ref. M. Kitazawa ,T. Koide,Y. Nemoto and T.K. Prog. of Theor. Phys., 108 , 929(2002). [ ３ ] C ×[ ３ ] C ＝ [ ３ ] C ＋ [ ６ ] C. 1 Introduction. Color Superconductivity(CSC). Cooper instability:.

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高密度クォーク物質における カイラル凝縮とカラー超伝導の競合

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  1. 高密度クォーク物質における カイラル凝縮とカラー超伝導の競合 国広　悌二(京大基研） 東大特別講義2005年12月5-7日 Ref. M. Kitazawa ,T. Koide,Y. Nemoto and T.K. Prog. of Theor. Phys., 108, 929(2002)

  2. [３]C×[３]C＝[３]C ＋[６]C 1Introduction Color Superconductivity(CSC) Cooper instability: In sufficiently cold fermionic matter, any attractive interaction leads to the instability to form infinite Cooper pairs. QCD at high density: asymptotic freedom Fermi surface attractive channel in one-gluon exchange interaction D.Bailin and A.Love, Phys.Rep.107,325(’84) Attractive! Ｔ Hadrons Cold, dense quark matter is color superconducting CSC morr 0

  3. Recent Progress in CSC (’98~) (mq < ms) ~ The di-quark gap D can become ~100MeV. M.Alford et al.,PLB422(’98)247 / R.Rapp et al.,PRL81(’98)53 / D.T.Son,PRD59(’99)094019 The possibility to observe the CSC in neutron stars or heavy ion collisions Another symmetry breaking pattern Color-flavor locked (CFL) phase at high density(mq >>ms) M.Alford ,K.Rajagopal, F.Wilczek,Nucl.Phys.B537(’98)443 CFL: 2SC: ｄ ｓ R.Pisarski,D.Rischke(’99) T.Schaefer,F.Wilczek(’99) K.Rajagopal,F.Wilczek(’00) ｄ ｕ ｄ ｕ ｓ ｄ ｕ ｄ ｕ ｕ

  4. Phase Diagram of QCD Ｔ End point of the 1st order transition M.Asakawa, K.Yazaki (’89) Chiral Symmetry Broken 2SC CFL μ 0 K. Rajagopal and F. Wilczek (’02), ”At the Frontier of Particle Physics / Handbook of QCD” Chap.35 Various models lead to qualitatively the same results. NJL-type 4-Fermi model Random matrix model Schwinger-Dyson eq. with OGE J.Berges, K.Rajagopal(’98) / T.Schwarz et al.(’00) B.Vanderheyden,A.Jackson(’01) M.Harada,S.Takagi(’02) / S.Takagi(’02) However, almost all previous works have considered only the scalar and pseudoscalar interaction in qq and qq channel.

  5. Vector Interaction density-density correlation The importance of the vector interaction is well known : Hadron spectroscopy Klimt,Luts,&Weise (’90) Chiral restoration Asakawa,Yazaki (’89) / Buballa,Oertel(’96) m Vector interaction naturally appears in the effective theories. Instanton-anti-instanton molecule model Shaefer,Shuryak (‘98) Renormalization-group analysis N.Evans et al. (‘99)

  6. Effects of GV on Chiral Restoration GV→Large First Order Cross Over As GV is increased, Chiral restoration is shifted to higher densities. The phase transition is weakened. Asakawa,Yazaki ’89 /Klimt,Luts,&Weise ’90 / Buballa,Oertel ’96

  7. Chiral Restoration at Finite m E E m Baryon density suppresses the formation of q-q pairing. 0 Chiral condensate ( q-q condensate ) 0 m:Small m:Large CSC ( q-q condensate ) Small Fermi sphere Large Fermi sphere leads to strong Cooper instability

  8. 2Formulation Nambu-Jona-Lasinio(NJL) model (2-flavors,3-colors): Parameters: current quark mass To reproduce the pion decay constant the chiral condensate Hatsuda,Kunihiro(’94) : is varied in the moderate range.

  9. Thermodynamic Potential in mean field approximation :chiral condensate :di-quark condensate Quasi-particle energies: cf.) s-w model

  10. Gap Equations The absolute minimum of w gives the equilibrium state. Gap equations ( the stationary condition): T=0MeV, m=314MeV GV=0 If there are several solutions, one must choose the absolute minimum for the equilibrium state.

  11. Effect of Vector Interaction on w = Contour map of w in MD-D plane = T=0 MeV m=314 MeV m small r large M large r small m Vector interaction delays the chiral restoration toward larger m.

  12. 3Numerical Results First Order Second Order Cross Over Phase Diagram The existence of the coex. phase Berges,Rajagopal(’98):×Rapp et al.(’00) : ○ Order Parameters MD :Chiral Condensate D :Diquark Gap

  13. As GV is increased… (1) The critical temperatures of the cSB and CSC hardly changes. It does not change at all in the T-r plane.

  14. (2) The first order transition between cSB and CSC phases is weakened and eventually disappears. (3) The region of the coexisting phase becomes broader. Appearance of the coexisting phase becomes robust. (4) Another end point appears from lower temperature, and hence there can exist two end points in some range of GV !

  15. Order Parameters at T=0 (in the case of chiral limit) Chiral restoration is delayed toward larger m. cSB survives with larger Fermi surface. Stronger Cooper instability is stimulated with cSB. The region of the coexisting phase becomes broader. 400 m[MeV] 300

  16. m Large fluctuation owing to the interplay between cSB and CSC is enhanced by GV. Contour of w with GV/GS=0.35 T= 22MeV 12MeV 15MeV 5MeV

  17. End Point at Lower Temperature As GV is increased, p pF cSB CSC Coexisting phase becomes broader . p pF D becomes larger at the phase boundary between CSC and cSB. The Fermi surface becomes obscure. This effect plays a role similar to the temperature, and new end point appears from lower T.

  18. Phase Diagram in 2-color Lattice Simulation J.B.Kogut et al. hep-lat/0205019

  19. Summary The vector interaction enhances the interplay between cSB and CSC. The phase structure is largely affected by the vector interaction especially near the border between cSB and CSC phases. Coexistence of cSB and CSC, 2 endpoints phase structure, Large fluctuation near the border between cSB and CSC Future Problems More deep understanding about the appearance of the 2 endpoints The calculation including the electric and color charge neutrality.

  20. Phase Diagram in the T-r plane

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