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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. 北沢 正清 大阪大学. 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. LHC. success of ideal hydro. models early thermalization. RHIC. strongly coupled QGP near T c. FAIR@GSI. Phase Diagram of QCD . T. Confined. Color SC. m. 0.

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北沢 正清 大阪大学

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  1. 盛岡研究会、つなぎ温泉、2009年6/26 カラー超伝導 北沢 正清 大阪大学 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. LHC • success of ideal hydro. models • early thermalization RHIC strongly coupled QGP near Tc FAIR@GSI Phase Diagram of QCD T Confined Color SC m 0

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

  4. Is There Quark Quasi-Particles in QGP? Yes, at asymptotically high T. Quark quasi-particles: normal • 2 collective excitations • having a “thermal mass” • mT~ gT w / mT “plasmino” • width G~g2T p / mT The decay width grows as T is lowered. NOT clear, near Tc.

  5. Similar result is obtained even with 1283x16! 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 Tc. Lattice QCD Simulation for Quarks Karsch, MK, 2007 Imaginary-time quark correlator in Landau gauge in quenched approx., 643x16 T = 3Tc 2-pole ansatz for quark spectral function: :normal :plasmino projection by tT

  6. Quark Dispersion Karsch, MK, arXiv:0906.3941. in quenched approx., 643x16 HTL(1-loop) (plasmino) p/T • Lattice results behave reasonably as functions of p. • Quarks have a thermal mass mT ~ 0.8T. (1.25<T/Tc<3) Notice: Similar result is obtained even with 1283x16! Decay width may be small even for V∞.

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

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

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

  10. Color Superconductivity at intermediate densities

  11. Color Superconductivity d s Dud u Dus Dds At extremely dense matter, quark (fermion) system attractive channel in one-gluon exchange interaction. [３]c×[３]c＝[３]c＋[６]c Cooper instability at sufficiently low T • pairing in scalar (JP=0+) channel color,flavor anti-symmetric T m

  12. d d s s Dud u Dus Dds Various Phases of Color Superconductivity T m Dud u Dus Dds 2-flavor SuperCondoctor (2SC) Color-Flavor Locking (CFL) analogy with B-phase in 3He superfluid

  13. d s Color Superconductivity in Compact Stars Dud u • effect of strange quark mass ms • neutrality and b-equilibrium conditions Dus Dds Mismatch of densities (1) strong coupling! (2) mismatched Fermi surfaces (1) weak coupling (2) common Fermi surface T m

  14. d s Various Phases of Color Superconductivity Dud 3 order parameters Dud, Dus, Dds  2*2*2=8 possibilities of distinct phases u Dus Dds cf.) Neumann, Buballa, Oertel ’03 + chiral symmetry restoration many phases at intermediate densities T Abuki, Kunihiro, 2005; Ruster et al.,2005; Fukushima, 2005 m

  15. d s Various Phases of Color Superconductivity Dud 3 order parameters Dud, Dus, Dds  2*2*2=8 possibilities of distinct phases u Dus Dds cf.) Neumann, Buballa, Oertel ’03 + chiral symmetry restoration many phases at intermediate densities T Abuki, Kunihiro, 2005; Ruster et al.,2005, Fukushima, 2005 m

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

  17. What is the True Ground State? gapless phases at T=0 have imaginary color Meissner masses mM2<0. Huang, Shovkovy,2003 Chromo-magnetic instability There is more stable state. Candidates of true ground state: • LOFF • gluonic phase • crystalline CSC • spin-one superconductivity • CSC + kaon condensation high  density  low

  18. d s Color Superconductivity in Compact Stars Dud • effect of strange quark mass ms u • neutrality and b-equilibrium conditions Dus Dds Mismatch of densities (1) strong coupling! (2) mismatched Fermi surfaces (1) weak coupling (2) common Fermi surface T m

  19. x / d m[MeV] x – coherence length d – interquark distance Structual Change of Cooper Pairs D ~ 100MeV T in electric SC D / EF ~ 0.1 D / EF ~ 0.0001 m Matsuzaki, 2000 Abuki, Hatsuda, Itakura, 2002

  20. bound diquarks for us, ds pairs 3-flavor NJL model w/ slightly strong coupling GD/GS=0.75 Phase Diagram mu,d=5MeV ms = 80MeV MK, Rischke, Shovokovy,2008 • m > m superfluidity • m < m vacuum: No BEC region. • Nevertheless, bound diquarks exist in the phase diagram.

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

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

  23. Conceptual Phase Diagram Conceptual phase diagram T Tdiss preformed stable bosons Tc superfluidity BEC BCS m ~ m weak coupling higher r strong coupling lower r large m

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

  25. 2-flavor NJL; GD/GS = 0.61 Pseudogap Region pseudogap region The pseudogap survives up to e =0.05~0.1 ( 5~10% above TC ). MK, et al., 2005

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

  27. Some Progress in Cold Atom

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

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

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

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

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

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

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