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Some aspects of p hase transition in dense quark matter

Some aspects of p hase transition in dense quark matter. Qun Wang University of Science and Technology of China. Phases in QCD Lattice results at finite temperature Dense baryonic matter Diquarks in cold baryonic matter. QCD phase transition and RHIC physics

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Some aspects of p hase transition in dense quark matter

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  1. Some aspects of phase transition in dense quark matter Qun Wang University of Science and Technology of China • Phases in QCD • Lattice results at finite temperature • Dense baryonic matter • Diquarks in cold baryonic matter QCD phase transition and RHIC physics Weihai, August9-14, 2009 1

  2. Research groups in China (QCD phase transition theory) 北大，清华 高能所 中科大 南大 华中师大 在职研究人员（2009.8） 教授、研究员：5±1人 副教授：2±1人 讲师、博士后：3±2人 2

  3. Phase diagram ofStrongly interacting Quark Gluon Plasma • See e.g. • Braun-Munzinger, Wambach, 2008 (review) • Ruester,Werth,Buballa, Shovkovy,Rischke,2005 • Fukushima, Kouvaris, Rajagopal, 2005 • Blaschke, Fredriksson, Grigorian, Oztas, Sandin, 2005 3

  4. Freezeout temperature and chemical potential in Heavy Ion Collisions Andronic, Braun-Munzinger, Stachel, 2006 Braun-Munzinger,Magestro,Redlich,Stachel, 2001 Cold baryonic matter 4

  5. Lattice QCD at finite temperature 5

  6. Lattice QCD at finite temperature Early papers: 0. Wilson, PRD1974 1. McLerran and Svetitsky, PLB1981,PRD1981 2. Kuti, Polonyi and Szlachanyi, PLB1981 3. Engels, Karsch, Montvay and Satz, PLB1981 6

  7. Lattice QCD at finite temperature Partition function of QCD lattice size 7

  8. n+μ+ν n+ν n n+μ Lattice QCD: gluon sector Gauge link Wilson action 8

  9. Lattice QCD: fermion sector The problem of fermion sector: 1. Fermion number doubling 2. Essential symmetries (chiral symmetry) of the continuum action are violated Solution: 1. Wilson fermion, add a higher derivative term 2. Staggered fermion, distribute components of the fermion Dirac spinors over several lattice sites, [Kogut and Susskind, PRD1975]. The Kogut-Susskind staggered fermion action: 9

  10. Lattice QCD partition function Wilson loop C reflect confinement property C 10

  11. Confinement C T: virtual time confining potential 11

  12. Polyakov Loop q at x q-bar at y Free energy for qq-bar Polyakov loop Polyakov loop as order parameter for phase transtion 12

  13. Deconfinement phase transition Center of SU(3)_c group 13

  14. Two phase phase transitions 1. chiral phase transition order parameter: chiral condensate well-define for 2. deconfinement phase transition order parameter: polyakov loop well-defined for 3. What happen to real world: 14

  15. Lattice QCD: Phase diagram Laerman,Philipsen, Ann.Rev.Nucl.Sci. 2003 15

  16. Lattice QCD: recent results arXiv:0903.4379 Bernard et al, (MILC) PRD 75 (07) 094505, Cheng et al, (RBC-Bielefeld) PRD 77 (08) 014511 Bazavov et al, (HotQCD),arXiv:0903.4379 16

  17. Lattice QCD: recent results Speed of sound 17

  18. Lattice QCD: recent results Chiral condensate Polyakov loop 18

  19. What viscosities will do? Shear viscosity: Bulk viscosity: -The velocity gradient are directly related to viscous behavior of the fluid -Viscosities reflect resistance to flow Y.G.Ma, Workshop on RHIC Physics andCSR physics, Weihai, 2009/8/9-14

  20. η/s around phase transition Lacey et al, PRL(2007) Lattice: Meyer, PRD(2007), PRL(2008)

  21. ζ/s around phase transition Karsch, Kharzeev, Tuchin PLB 2008 Noronha ^2, Greiner, 2008 Chen, Wang, PRC 2009 ......

  22. η/s of gluon gas -- variation method Variation method: Chen, Dong, Ohnishi, Wang, arXiv:0907.2486 Cascade model: Xu, Greiner, PRL(2008)

  23. Ratio of 22+23/22 of gluon gas --variation method Variation method: Chen, Dong, Ohnishi, Wang, arXiv:0907.2486 Cascade model: Xu, Greiner, PRL(2008)

  24. Dense baryonic matter 24

  25. Dense baryonic matter 1. non-perturbative method lattice QCD, Dyson-Schwinger eq., AdS/QCD [Y.X. Liu, H.S. Zong, ......] 2. effective models chiral perturbation theory chiral models (NJL, linear-σ, etc) [P.F. Zhuang, Y.X.Liu, M. Huang, Q.Wang, ......] 3. Perturbative method [D.F.Hou, Q.Wang, ......] 25

  26. NJL + Polyakov = PNJL Fukushima,PLB 2004; Ratti, Thaler, Weise, PRD 2006; Zhang, Liu, PRC 2007 ...... constant field, Polyakov gauge 26

  27. NJL-part gluonic part NJL + Polyakov = PNJL Thermodynamical potential inspired by lattice result

  28. PNJL: Gap equation parameters

  29. PNJL: results K. Fukushima, PRD 2008

  30. PNJL: results critical point (NJL): (T,μ)=(48,324) MeV (PNJL): (T,μ)=(102,313) MeV K. Fukushima, PRD 2008

  31. Diquark in baryonic matter --from weak to strong couplings 31

  32. Why color superconductivity Anti-symmetric channel: attractive interaction Energy gap in quasi-particle excitation 32

  33. Color superconductivity - weak coupling Weak coupling gap equation (DS equation) in asymptotically high density 33

  34. Weak coupling solution to gap equation [Son 1999; Schafer,Wilczek 2000; Hong et al. 2000; Pisarski,Rischke 2000; Brown et al 2000; Wang,Rischke 2002; Schmitt,Wang,Rischke 2003] 34

  35. Pairings within the same flavor Schmitt, QW, Rischke, Phys.Rev.Lett.91, 242301(2003) Schmitt, Phys.Rev.D71, 054016(2005) 35

  36. Meissner effects in weak coupling Son, Stephanov, Phys.Rev.D61,074012(2000); Schmitt, QW, Rischke, Phys. Rev. D69, 094017(2004); Phys. Rev. Lett.91, 242301(2003) 36

  37. Meissner effects in weak coupling: results Schmitt, QW, Rischke, PRL(2003) ■ Rotated photon in CSL phase has a non-vanishing mass: Electromagnetic Meissner effect. ■ Although rotated photon in polar phase has a zero mass but a system with 2 or 3 favors still exhibits Electromagnetic Meissner effect because of different chemical potential or no single mixing angle for all favors. 37

  38. Effective Theory of dense matter • Controlled calculation in QCD • physics dominated by strip close to Fermi surface • separation of scales and need for EFT Hong, 2000 Schaefer, 2002, 2003 Reuter, QW, Rischke, 2004 38

  39. It (QCD) provides the answer to a child-likequestion: What happens to matter, as you squeeze it harder and harder? -- Wilczek Answer: Perturbation in QCD in weak coupling An oppositequestion: What happens to matter, as you increase interactions stronger and stronger? What happens to quark-quark pairings: do they survive stronger and stronger interactions? Answer: unclear 39

  40. BCS-BEC Crossover Science 40

  41. Relativistic BCS-BEC crossover • Recent works by other group: • Nishida & Abuki, PRD 2007 -- NJL approach • – Abuki’s Talk • Abuki, NPA 2007 – Static and Dynamic properties • Sun, He & Zhuang, PRD 2007 –NJL approach • He & Zhuang, PRD 2007 – Beyond mean field • Kitazawa, Rischke & Shovkovy, arXiv:0709.2235v1 – NJL+phase diagram • – Kitazawa’s Talk • Brauner,arXiv:0803.2422 – Collective excitations • – Brauner’s Talk • Chatterjee, Mishra, Mishra, arXiv:0804.1051 -- Variational approach 41

  42. Relativistic boson-fermion model (MFA) With bosonic and fermionic degrees of freedom and their coupling, but neglect the coupling of thermal bosons and fermions as Mean Field Approximation Friedberg-Lee model, 1989 zero mode of boson 42 J. Deng, A. Schmitt, QW, Phys.Rev.D76:034013,2007

  43. Thermodynamic potetial 43

  44. Density and gap equations Crossover parameter x<0, BCS regime x>0, BEC regime 44

  45. At zero T or critical T 45

  46. Dispersion relation In BCS regime, fermions are slightly gapped, anti-fermions are strongly gapped. In BEC regime, both are strongly gapped, indicating the formation of bound states with large binding energy 46

  47. Unitary Regime 47

  48. Pairing with imbalance population --Fermi surface topologies 48

  49. Homogeneous solution The fermion-boson mixture in BCS-BEC regime has been found in cold atomic system. Stable gapless phase in strong coupling (see also Kitazawa,Rischke, Shovkovy, 2006) [ Realization of a strongly interacting Bose-Fermi mixture from a two-component Fermi gas, MIT group, arXiv:0805.0623 ] 49

  50. Phase diagram Non-relativistic relativistic Shaded area: unstable, with negative susceptibility 50

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