1. Masakiyo Kitazawa Osaka University ATHIC2008, Tsukuba, Oct. 14, 2008 “strongly coupled” Quark Matter

2. Phase Diagram of QCD T 0 Confined Color SC strongly coupled QGP @ RHIC Quark matter at intermediate  will be a strongly coupled system, too. “strongly coupled” color superconductor will be realized. 

3. Phase Diagram of QCD T 0 Confined Color SC strongly coupled QGP @ RHIC Quark matter at moderate  will be a strongly coupled system, too. “strongly coupled” color superconductor will be realized. Shuryak, PoS, CPOD2006:026 

4. Quark Quasi-particles in the Deconfined Phase Quark Quasi-particles in the Deconfined Phase

5. 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.

6. Lattice QCD Simulation for Quarks Lattice result is well reproduced by 2-pole ansatz (  2 /dof~1). Quark excitations would have small decay rate even near T c. 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 See also the analysis in SD eq., Harada, Nemoto, 2007

7. Quark Dispersion HTL(1-loop) p/T Karsch, MK, to appear soon. (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: Further studies on spatial volume and discretization effects are needed for the definite conclusion about .

8. 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

9. Phase Diagram T  0 0 th approximation: (quasi-)fermions + interaction (gluon-ex.) crossover transition quarkyonic region McLerran, Pisarski, 2007 chirally restored but confined quark-hadron continuity quark-diquark model / trionic liquid / etc… Is thermal mass m T ~0.8T not negligible?  See, Hidaka, MK 2007 (topics NOT considered here) analogy to condensed matter phys. Polarized gas BCS-BEC crossover strongly correlated system

10. Color Superconductivity and Polarized Fermi Gas Color Superconductivity and Polarized Fermi Gas

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. 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

14. 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 

15. 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

16. 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 

17. 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

18. 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

19. 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

20. Various Efforts 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… Talks byShijun Mao Lianyi He

21. BCS-BEC Crossover of CSC and Diquark Fluctuations in the Quark Matter BCS-BEC Crossover of CSC and Diquark Fluctuations in the Quark Matter

22. preformed stable bosons Nozieres, Schmitt-Rink Conceptual Phase Diagram weak coupling higher  m~0 strong coupling lower  large m BCS BEC T m ~  superfluidity TcTc T diss “Hidden” because of  =0 or by confinement Shuryak, PoS, CPOD2006:026 Dissociation T = zero binding line Shuryak, Zahed, 2004

23. preformed stable bosons Nozieres, Schmitt-Rink Conceptual Phase Diagram weak coupling higher  m~0 strong coupling lower  large m BCS BEC T m ~  superfluidity TcTc T diss How strong is the coupling before the confinement? Is it sufficient to realize BEC? Are there bound diquarks in the QGP phase? “Hidden” because of  =0 or by confinement

24. Stability of Diquarks above T c m11m11 m22m22 (2) Threshold energy of diquarks are (1) The pole is at  =0 at T=T c (Thouless criterion).  > m 0   < m 0  No stable diquarks above T c Stable diquarks exist above T c until T diss  <m is the criterion for BEC. Nozieres, Schmitt-Rink ’85 Dynamically generated quark masses determine the stability. Nozieres, Schmitt-Rink, 1985 Nishida, Abuki, 2007 Note: Thermal mass is not responsible for the stability. Hidaka, MK, 2007

25. 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

26. 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

27. 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 ~ 

28. 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 ~ 

29. Pole of Diquark Propagator above T c  > m 0  < m 0 BEC region TcTc T diss Weak coupling MK, et al., 2002 TcTc weak coupling limit

30. 0 0 TcTc T diss TcTc weak coupling limit Pole of Diquark Propagator above T c  > m  < m BEC regionWeak coupling MK, et al., 2002 2-flavor;G D /G S = 0.61

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

32.  0 ( ,k)  = 400 MeV  =0.01 k  0  [MeV] quasi-particle peak,  =    k)~ k  Depression at Fermi surface k [MeV] kFkF kFkF Quark Spectral Function MK, et al., 2005 T-matrix approximation Diquark fluctuations largely modify quark excitations.

33. 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

34. 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 ~ 

35. dR ee /dM 2 [fm -4 GeV -2 ] invariant mass M [MeV] How to Measure Diquarks Fluctuations? Dilepton production rate Recombination Lee, et al., 2008  = 400MeV Dilepton rate from CFL phase  Jaikumar,Rapp,Zahed,2002 Aslamasov-Larkin term

36. Summary The quenched lattice simulation indicates the existence of the quark quasi-particles even near T c, having a thermal mass m T ~0.8T. The quark matter under neutrality conditions has an extremely rich phase structure owing to the mismatches of Fermi surfaces. The formation of superconductivity in the polarized gas is a hot topics in the condensed matter physics, and the QM community will have a lot to learn from them. If the diquark coupling is strong enough, the quarks form stable diquarks in the QGP phase at lower . Even if the diquark coupling is not sufficiently strong, the fluctuations affect various observables near but well above T c.

37. 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

38. 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 ~ 