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Heating (Gapless) Color-Flavor Locked Quark Matter

Heating (Gapless) Color-Flavor Locked Quark Matter. Understanding the Phase Diagram of Dense Quark Matter. Kenji Fukushima (MIT / U.Tokyo). Ref : K. Fukushima, C. Kouvaris, and K. Rajagopal, hep-ph/0408322 to appear in Phys.Rev.D. QCD Phase Diagram.

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Heating (Gapless) Color-Flavor Locked Quark Matter

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  1. Heating (Gapless) Color-Flavor Locked Quark Matter Understanding the Phase Diagram of Dense Quark Matter Kenji Fukushima (MIT / U.Tokyo) Ref : K. Fukushima, C. Kouvaris, and K. Rajagopal, hep-ph/0408322 to appear in Phys.Rev.D

  2. QCD Phase Diagram In the m-T plane . . . various phases! From an NJL model. Color and electricneutral quark matterwith Ms=150MeV fixed. Quantitative featuresdepend on the model. Qualitative natureis robust.

  3. Color-Flavor Locked (CFL) Phase Cooper Instability DegeneratedFermi sphere Attractive interaction Diquark Condensate Cooper pair Superconductor ud su ds Energetically favored diquarks areColor-triplet (anti-symmetric) and Spin-0 (anti-symmetric). Flavor-triplet (anti-symmetric) Ms effects can make the gap parameters asymmetric .

  4. Gap Parameters

  5. Strange Quark Mass Effects

  6. Color and Electric Neutrality Chemical Potential Neutrality Conditions Electronless and cold CFL quark matter is a insulator : or W does not depend on

  7. Gapless CFL Phase Parameters d u s

  8. Stability Conditions gCFL at low temperatures (bd-gs) (rs-bu) (gu-rd) Instability occurs at this critical value of Ms .

  9. Blocking Region gs corresponds tothe onset of the gapless dispersion relations even with a finite gap. bd Gapless Quark Excitations

  10. On the Phase Diagram

  11. Small m (large Ms ) at low T T = 4MeV 2SC window opens. D1 goes to zero first uSC phase

  12. Large m (Small Ms) near Tc d u D2 goes to zero first dSC phase s

  13. On the Phase Diagram The presence of dSCis robust, though itmight disappeardue to the cut-offartifact. (Ruster-Shovkovy -Rischke ’04) Doubly Critical Point Consistent withthe GL approachwith QCD outputs. (Iida et al. ’03)

  14. Symmetry Breaking Pattern (Global) Symmetry Breaking () Asymmetric Quark Matter ( ) In unpaired quark matter In the mCFL phase In the uSC (dSC) phase No UB(1) Nambu-Goldstone boson (phonon) in the uSC (dSC) phase

  15. Summary • Phase diagram of neutral quark matter • CFL, gCFL, uSC, dSC, 2SC, UQ appear • Gap parameter ordering • D1<D2<D3 in the gapless CFL phase • Neutrality conditions + Fermi surface discrepancies • D2<D1<D3 in the CFL phase near Tc • Neutrality conditions + Average Fermi surface ordering • Symmetry breaking pattern • CFL uSC (dSC) characterized by U(1)

  16. Appendices The following is only for questions.

  17. Cold Neutral CFL Alford-Rajagopal JHEP 0206, 031 (2002) Steiner-Reddy-Prakash PRD 66, 094007 (2002) ~ me is arbitrary due to Q insulator. In the presence of the electron contribution, ~ me= 0 is favored. [Not “Q insulator” with the electron.] Electronless CFL can be color and electric neutral.

  18. Modified Electromagnetism Unbroken U(1) symmetry in CFL generated by CFL quark matter is a insulator. No excitation with non-trivial .

  19. Intuitive Picture BCS ansatz requires the same number of quarks in each pairing sector. Same Same Same m8 When the Cooper pair becomes unstable energetically,the neutral quark matter enters a new phase.

  20. Computational Procedures Four-quark interaction Approximations • Symmetric (sextet) condensates are neglected. • Chiral symmetry is assumed to be restored.‘t Hooft term is dropped. • Meson condensations are not considered.

  21. Thermodynamic Potential ej(p) are the eigenvalues of the 72x72 inverse propagator (color=3 x flavor=3 x spin=4 x Nambu-Gor’kov=2)

  22. Cutting the Phase Diagram Cut here

  23. Chemical Potentials In the CFL phase,

  24. First-Order Phase Transition A first-order phase transition from gCFL to unpaired QM at Ms2/m =125MeV.

  25. Different Choice of G Parameters The nature of the first-order phase transition strongly depends on the coupling constant. 2SC window opens.

  26. Different Choice of G Further Parameters The number density of strange quarks is zero for larger Ms. No first-order phase transition.

  27. Cutting the Phase Diagram Cut here

  28. Ms2/ m= 70MeV

  29. Cutting the Phase Diagram Cut here

  30. Ms2/ m= 130MeV

  31. Analytical Approaches Two important features Insulator-metal crossover near T ~ 0 dSC phase near T ~ Tc (GL approach)

  32. Insulator-Metal Crossover Chemical Potentials at me is small first, then rapidly increases, and is saturated finally. Clear crossover is seen. (Insulator to Metal)

  33. T = 2MeV me is saturated at Ms2/4m

  34. Analytic Evaluation ~ CFL matter remains to be almost a Q insulator. me is determined by the balance between * electric contribution to W * thermal excitation of quasi-quarks [only (rs-bu) and (gu-rd) quarks with ] * thermal excitation of charged mesons This will be considered later.

  35. Thermal Excitations of Quarks Dispersion Relations Saddle-Point Approximation Results

  36. Comparison Excellent agreement! At small T, the exponential factor is small enough. me stays small. At larger T, sinh must be small too. me is saturated at Ms2/4m

  37. Inclusion of Charged Mesons If the instanton contribution to the K mass is large enough (~50MeV), K is so heavy that there is no K condensation and the thermal excitation is safely negligible.

  38. Existence of the dSC Phase Ratio between the three slopes 1 : 10.1 : 19.1 This should be described by the Ginzburg Landau approach.

  39. Ginzburg-Landau Approach K.Iida et al, hep-ph/0312363 Ginzburg-Landau approach is valid near Tc Ratio between the slopes is determined by two parameters z =e /h and b1/b2.

  40. Mean-Field Approximation b1=b2 e(direct Ms effect) h(me effect)

  41. Ginzburg-Landau Approach VII The ratio of the slopes from the GL approach is 1 : 6z -5 : 6z+4 = 1 : 10.1 : 19.1 with the parameter z =2.52 calculated from the diagrams.

  42. Summary • Phase diagram involving CFL, gCFL, uSC, dSC, 2SC is investigated. • uSC-2SC boundary at low T is strongly dependent on the coupling constant. • Insulator-to-Metal crossover in the CFL phase is described analytically. • Consistency with the Ginzburg-Landau approach is confirmed. dSC exists robustly. • Doubly critical point is pointed out.

  43. Future Problems • Stability problem • Chiral phase transition (physical Ms) • K0 condensation • Application to observables • Proto-neutron star (T=30~50MeV)

  44. More Phase Diagrams Stronger and stronger coupling constant

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