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Masakiyo Kitazawa Osaka University

ATHIC2008, Tsukuba, Oct. 14, 2008. “ s trongly coupled” Quark Matter. Masakiyo Kitazawa Osaka University. strongly coupled QGP @ RHIC. Quark matter at intermediate m will be a strongly coupled system, too. “strongly coupled” color superconductor will be realized.

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Masakiyo Kitazawa Osaka University

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

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

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

  4. Quark Quasi-particles in the Deconfined Phase

  5. 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.

  6. 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 • Lattice result is well reproduced by 2-pole ansatz (c2/dof~1). Quark excitations would have small decay rate even near Tc. See also the analysis in SD eq., Harada, Nemoto, 2007

  7. Quark Dispersion Karsch, MK, to appear soon. 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: Further studies on spatial volume and discretization effects are needed for the definite conclusion about G.

  8. 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

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

  10. Color Superconductivity and Polarized Fermi Gas

  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. 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

  14. 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

  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. 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

  17. 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

  18. 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

  19. 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?

  20. Various Efforts • 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 Talks by Shijun Mao Lianyi He polarization

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

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

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

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

  25. 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.

  26. 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.

  27. 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

  28. 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

  29. Pole of Diquark Propagator above Tc BEC region Weak coupling m < m m > m Tc Tdiss Tc 0 0 weak coupling limit MK, et al., 2002

  30. Pole of Diquark Propagator above Tc BEC region Weak coupling m < m m > m Tc Tdiss Tc 0 0 weak coupling limit 2-flavor;GD/GS = 0.61 MK, et al., 2002 MK, et al., 2002

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

  32. Depression at Fermi surface Quark Spectral Function m = 400 MeV e =0.01 r0(w,k) quasi-particle peak, w =w-(k)~ k-m w k 0 w [MeV] k[MeV] kF MK, et al., 2005 kF T-matrix approximation • Diquark fluctuations largely modify quark excitations.

  33. 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

  34. 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

  35. Recombination Lee, et al., 2008 How to Measure Diquarks Fluctuations? Dilepton production rate m = 400MeV dRee/dM2 [fm-4GeV-2] invariant mass M [MeV] 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 Tc, having a thermal mass mT~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 m. • Even if the diquark coupling is not sufficiently strong, • the fluctuations affect various observables near but well above Tc.

  37. 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

  38. 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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