1. 北沢 正清 大阪大学 盛岡研究会、つなぎ温泉、 2009 年 6/26 カラー超伝導 Contents: (1) クォーク (2) 低～中間密度領域のカラー超伝導 (3) 冷却原子系からの情報

2. Phase Diagram of QCD T 0 RHIC success of ideal hydro. models early thermalization strongly coupled QGP near T c Confined Color SC  LHC FAIR@GSI

3. Quark “Quasi-particles” in the Deconfined Phase Quark “Quasi-particles” in the Deconfined Phase

4. Is There Quark Quasi-Particles in QGP? Is There Quark Quasi-Particles in QGP? “plasmino” p / m T  / m T Yes, at asymptotically high T. 2 collective excitations having a “thermal mass” m T ~ gT width  ~g 2 T normal Quark quasi-particles: The decay width grows as T is lowered. NOT clear, near T c.

5. Lattice QCD Simulation for Quarks Karsch, MK, 2007 2-pole ansatz for quark spectral function: :normal :plasmino Imaginary-time quark correlator in Landau gauge in quenched approx., 64 3 x16 TT T = 3T c projection by Similar result is obtained even with 128 3 x16! MK et al. in preparation. Result is insensitive to # of data points used in the analysis. Quark excitations would have small decay rate even near T c.

6. Quark Dispersion HTL(1-loop) p/T Karsch, MK, arXiv:0906.3941. (plasmino) Lattice results behave reasonably as functions of p. Quarks have a thermal mass m T ~ 0.8T. (1.25<T/T c <3) in quenched approx., 64 3 x16 Notice: Similar result is obtained even with 128 3 x16!  Decay width may be small even for V  ∞.

7. Phase Diagram T  0 0 th approximation: (quasi-)fermions + interaction (gluon-ex.) analogy to condensed matter phys. Polarized gas BCS-BEC crossover strongly correlated system Is thermal mass m T ~0.8T not negligible?  See, a trial in Hidaka, MK 2007

8. Phase Diagram T  0 0 th approximation: (quasi-)fermions + interaction (gluon-ex.) crossover transition quarkyonic region McLerran, Pisarski, 2007 chirally restored but confined Is thermal mass m T ~0.8T not negligible?  See, a trial in Hidaka, MK 2007 analogy to condensed matter phys. Polarized gas BCS-BEC crossover strongly correlated system

9. Phase Diagram T  0 0 th approximation: (quasi-)fermions + interaction (gluon-ex.) crossover transition quarkyonic region McLerran, Pisarski, 2007 chirally restored but confined Are 2 phases connected continuously at lower T? 1 st CP : Asakawa, Yazaki, 1989. 2 nd CP : MK, et al., 2002 (See, also Yamamoto, et al., 2006). 3 rd CP : Zhang, et al.,2009. analogy to condensed matter phys. Polarized gas BCS-BEC crossover strongly correlated system

10. Color Superconductivity at intermediate densities Color Superconductivity at intermediate densities

11. Color Superconductivity Color Superconductivity pairing in scalar (J P =0 + ) channel color,flavor anti-symmetric T  attractive channel in one-gluon exchange interaction. quark (fermion) system Cooper instability at sufficiently low T [ ３ ] c ×[ ３ ] c ＝ [ ３ ] c ＋ [ ６ ] c At extremely dense matter, ud s  ud  us  ds

12. Various Phases of Color Superconductivity ud s  ud  us  ds u d s  ud  us  ds Color-Flavor Locking (CFL)2-flavor SuperCondoctor (2SC) analogy with B-phase in 3 He superfluid T 

13. Color Superconductivity in Compact Stars u d s (1) strong coupling! (2) mismatched Fermi surfaces (1) weak coupling (2) common Fermi surface  ud  us  ds effect of strange quark mass m s neutrality and  -equilibrium conditions Mismatch of densities T 

14. Various Phases of Color Superconductivity u d s  ud  us  ds  2  2  2=8 possibilities of distinct phases  ud =  us =  ds >0 CFL Alford, et al. ‘98  ud >0,  us =  ds =0 2SC Bailin, Love ‘84 + chiral symmetry restoration 3 order parameters  ud,  us,  ds  ud >0,  us >0  ds =0 uSC Ruster, et al. ‘03  ud >0,  ds >0  us =0 dSC Matsuura, et al., ‘04 cf.) Neumann, Buballa, Oertel ’03 many phases at intermediate densities T  Abuki, Kunihiro, 2005; Ruster et al.,2005; Fukushima, 2005

15. Abuki, Kunihiro, 2005; Ruster et al.,2005, Fukushima, 2005 Various Phases of Color Superconductivity u d s  ud  us  ds  2  2  2=8 possibilities of distinct phases  ud =  us =  ds >0 CFL Alford, et al. ‘98  ud >0,  us =  ds =0 2SC Bailin, Love ‘84 + chiral symmetry restoration 3 order parameters  ud,  us,  ds  ud >0,  us >0  ds =0 uSC Ruster, et al. ‘03  ud >0,  ds >0  us =0 dSC Matsuura, et al., ‘04 cf.) Neumann, Buballa, Oertel ’03 many phases at intermediate densities T 

16. Sarma Instability The gapless SC is realized only as the maximum of the effective potential. gapless BCS Sarma instability n p p Gapless state is unstable against the phase separation. unlocking region

17. What is the True Ground State? LOFF gluonic phase crystalline CSC spin-one superconductivity CSC + kaon condensation Candidates of true ground state: gapless phases at T=0 have imaginary color Meissner masses m M 2 <0. Chromo-magnetic instability There is more stable state. Huang, Shovkovy,2003 high  density  low

18. Color Superconductivity in Compact Stars (1) strong coupling! (2) mismatched Fermi surfaces (1) weak coupling (2) common Fermi surface effect of strange quark mass m s neutrality and  -equilibrium conditions Mismatch of densities T  u d s  ud  us  ds

19. Structual Change of Cooper Pairs T  Matsuzaki, 2000 Abuki, Hatsuda, Itakura, 2002  [MeV]  d  – coherence length d – interquark distance  ~ 100MeV  / E F ~ 0.1  / E F ~ 0.0001 in electric SC

20. Phase Diagram  > m  superfluidity  < m  vacuum: No BEC region. Nevertheless, bound diquarks exist in the phase diagram. 3-flavor NJL model w/ slightly strong coupling G D /G S =0.75 MK, Rischke, Shovokovy,2008 bound diquarks for us, ds pairs m u,d =5MeV m s = 80MeV

21. Phase Diagram at Strong Coupling BEC manifests itself. Bound diquarks would exist in the deconfined phase. G D /G S =1.1 BEC MK, Rischke, Shovokovy,2008

22. Conceptual Phase Diagram weak coupling higher  strong coupling lower  large m BCS BEC T preformed stable bosons Conceptual phase diagram superfluidity TcTc T diss hidden by mass discontinuity at 1 st order transition m ~ 

23. Conceptual Phase Diagram weak coupling higher  BCS BEC T preformed stable bosons Conceptual phase diagram superfluidity TcTc T diss strong coupling lower  large m m ~ 

24. Pseudogap in HTSC Depression of the DoS around the Fermi surface above T c Pseudogap

25. The pseudogap survives up to  =0.05~0.1 ( 5~10% above T C ). pseudogap region Pseudogap Region 2-flavor NJL; G D /G S = 0.61 MK, et al., 2005

26. Conceptual Phase Diagram weak coupling higher  strong coupling lower  large m BCS BEC T preformed stable bosons Conceptual phase diagram superfluidity TcTc T diss Pseudogap (pre-critical) region T* m ~ 

27. Some Progress in Cold Atom

28. Crossover in Polarized Fermi gas Pao, Wu, Yip, cond-mat/0506437 Son, Stephanov, cond-mat/0507586 Question: How is the intermediate region between two limits in the polarized Fermi gas? homogeneous mixture of fermions and bound bosons Strong coupling limit Weak coupling limit spatially inhomogeneous LOFF phase separation

29. Various Efforts in Cold Atom Society T/T F polarization Shin, et al., Nature451,689(2008) Experimental result at unitarity in the trapped gas —no polarized SC at unitarity Monte Carlo simulation Renormailzation group method etc…

30. Cold Fermions with N Species Trapped potential + optical trap Select N hyperfine states w/ magnetic trap N-”flavor” attractive fermion system E for N=3,

31. Cold Fermions with N Species Trapped potential + optical trap Select N hyperfine states w/ magnetic trap N-”flavor” attractive fermion system E for N=3, weak coupling: “2SC” BCS state strong coupling: Fermi-liquid of “trions” phase transition

32. Trion-BCS Transition 3-component Hubbard model: Rapp, et al., PRL99,130406(2007). Rapp, et al., PRB77,144520(2008). Gutzwiller ansatz: MFA for g and  BCS large d limit weak strong Fermion-boson mixture : Another interesting system Maeda, et al., 0904.4372 fermion boson attraction Strong coupling superfluid molecules Weak coupling BEC of bosons

33. Summary QCD 相転移の向こう側ではクォーク物質（もしくは QGP 状 態）が実現しており、低温高密度の基底状態はカラー超伝導 である。 低密度領域のカラー超伝導は強結合系であり、かつフェルミ 面が不揃いな超伝導状態である。 冷却原子系から得られる情報は極めて興味深く、 QCD 相図 および、ハドロン化のメカニズムを理解する上でも有用な可 能性がある。

34. Summary weak coupling higher  BCS BEC T preformed stable bosons Conceptual phase diagram superfluidity TcTc T diss Pseudogap (pre-critical) region T* RHIC; hadronization, etc. measurement on lattice QCD FAIR@GSI? Bound diquark would exist in sQGP. Large fluctuations affect various observables. strong coupling lower  large m m ~ 