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Thermal phase transition of color superconductivity with

Thermal phase transition of color superconductivity with Ginzburg-Landau effective action on the lattice. M. Ohtani ( RIKEN ) with S. Digal ( Univ. of Tokyo ) T. Hatsuda ( Univ. of Tokyo ). Introduction GL effective action Phase diagram in weak gauge coupling

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Thermal phase transition of color superconductivity with

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  1. Thermal phase transition of color superconductivity with Ginzburg-Landau effective action on the lattice M. Ohtani (RIKEN) with S. Digal (Univ. of Tokyo) T. Hatsuda (Univ. of Tokyo) • Introduction • GL effective action • Phase diagram in weak gauge coupling • Phase transition on the lattice • Summary XQCD, Aug 2 @ Swansea

  2. Δ ~ 100MeV Tc ~ 60MeV Introduction Ｔ RHIC Quark-Gluon Plasma 170MeV Hadrons Color Superconductivity   qq   0 N ☆ Cores μ ~400MeV • Non-perturbative analysis of colorsuper transition

  3. { ¶ no sign problem bosonic T-m dependence: m, li ,k,g ( discretize & rescale SUf (3) SUc(3) Higgs on Lattice ○ ○ ○ 2 couplings for quartic terms Ginzburg-Landau effective action Iida & Baym PRD 65 (2002)014022 GL action in terms of the quark pair field Ffc (x) & gauge field

  4. l1 = l2 in weak coupling mean field without gluon Iida & Baym PRD 63 (2001)074018 mean field (ungauged) l2 normal  CFL as T D F~D D l1 F = 0 normal  2SC unbound @ Tc(MF) 0 F~0 D 2nd order transition

  5. l2 normal  CFL normal2SCCFL l1 normal 2SC unbound 1st order transition weak gauge coupling limit Matsuura,Hatsuda,Iida,Baym PRD 69 (2004) 074012 mean field (ungauged) perturbative analysis l2 Normal  CFL gluonic fluctuation l1 |F |3 term normal2SC unbound 2nd order transition

  6. Phase diagram in weak gauge coupling CFL 2SC normal 1-T/Tc(MF)~k l2 unbound l1

  7. Phase diagram in weak gauge coupling

  8. l2 normal  CFL normal2SCCFL l1 normal 2SC unbound Analytic results for large  mean field (ungauged) perturbative analysis l2 Normal  CFL gluonic fluctuation l1 normal2SC unbound 2nd order transition 1st order transition

  9. Setup for Monte-Carlo simulation parameters { b = 5.1 0.7 bc in pure YM take several pairs of (l1, l2 ), scanning k Lattice size Lt = 2 , Ls = 12, 16, 24, 32, 40 with 3,000－60,000 configurations update pseudo heat-bath method for gauge field generalized update-algorithm of SU(2) Higgs-field Bunk, NP(Proc.Suppl) 42 (‘95), 556 @ RIKEN Super Combined Cluster

  10. phase transition to ‘color super’ ¶ Tr Fx†Fx¹ 0 even in sym. phase thermal fluctuation  broken phase plateau jump @ kc Phase identification Tr Fx†Fx (Tr F†F )1/2 update step large order param. ⇔ broken phase

  11. F†FI・・・CFL a F†F~b ・・・2SC b ¶ F†F : gauge invariant diagonalization identifying the phases by eigenvalues of FyF matrix elements of F†F

  12. Phase diagram with li fixed k CFL Color Superconducting state ● Similar trends with SU(2) Higgs ● no clear signal of end points as li 0.16 2SC normal (Quark-Gluon Plasma) 0.08 l1 =l2 =.0005 Hadron b 5.6 5.1 3.6 4.8

  13. Hysteresis : different configs. with same k  CFL ß Put 3 configs in spatial sub-domain 2SC ß Thermalize it with fixed k 1st order transition: Hysteresis & boundary shift initial config. = a thermalized config. with slightly different k CFL 2SC Polyakov loop normal k

  14. perturbative analysis l2 CFL 2SCCFL l1 2SC unbound Phase diagram with b fixed lattice simulation l2 CFL CFL w/metastable 2SC 2SC CFL metastable 2SC: 2SC observed in hysteresis & disappeared in boundary shift test 2SC l1 1st order transition

  15. ●largest barrier btw normal &CFL ●$metastable 2SC Free energy by perturbation Iida,Matsuura,Tachibana,Hatsuda PRD 71 (2005)054003 D1 = D2 2 D1 F†F~D1 D3 CFL normal 2SC D3

  16. Summary and outlook • GL approach with quark pair field F & gauge on lattice •  SU(3) Higgs model • eigenvalues of F†F to identify the phases 1st order trans. toCFL & 2SC phases in coupling space • We observed hysteresis. transition points boundary shift with mixed domain config. • $metastable 2SC state in transition from normal to CFL, which is consistent with perturbative analysis • charge neutrality, quark mass effects, correction to scaling, phase diagram in T-m, …

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