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Thermal phase transitions in realistic dense quark matter

Thermal phase transitions in realistic dense quark matter. Taeko Matsuura (Tokyo) K. Iida (RIKEN BNL) M. Tachibana (RIKEN) T. Hatsuda (Tokyo). Physical Review Letters 93 (2004) 132001 hep-ph/0411356 (to appear in PRD).

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Thermal phase transitions in realistic dense quark matter

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  1. Thermal phase transitions in realistic dense quark matter Taeko Matsuura (Tokyo) K. Iida (RIKEN BNL) M. Tachibana (RIKEN) T. Hatsuda (Tokyo) Physical Review Letters 93 (2004) 132001 hep-ph/0411356 (to appear in PRD)

  2. Realistic QCD phase diagram(Nf=3) Idealized QCD phase diagram (Nf=3) mu,d ~0 and ms ~200 MeV beta equilibrium charge neutral “external fields” T T dm mu,d,s =0 QGP QGP 2SC dSC mCFL Hadron Hadron Color superconductor (CFL) μ μ

  3. Examples of new phases driven by external fields unequal Fermi moms for ( ) and ( )

  4. Color Superconductor (without m, dm ) Entangled pairing in color-flavor space (momentum)

  5. quark mass ms >> mu,d 0, • beta equilibrium d m i= －qime (i=u, d, s) • electric neutrality Q＝Qquark +Qelectron=0 • color neutrality nR＝ nB＝ nG major role minor role Realistic quark matter at T~Tc Why we consider T~Tc ? Effect of the ext. field (m, dm )prominent Ginzburg-Landau expansion possible (Δ<< Tc )

  6. Tc ms2 μ Color Superconductor (with m, dm ) near Tc Ext. fields: ・ What kind of phase structure near Tc? ・ What are the quark & gluon spectra ?

  7. Δ Δ T>Tc T<Tc Corrections from quark mass & charge neutrality Corrections from color neutrality Ginzburg-Landau free energy Near Tc (Δ << Tc)

  8. High density QCD → GL free energy small external fields • m=0, dm=0Iida & Baym, PRD (`01)

  9. m≠0, dm≠0 Iida,Matsuura,Tachibana,&Hatsuda, PRL (2004) O(Δ2ms2) Flavor Flavor dependent shift of the GL free energy

  10. shift of critical temperature Larger averaged Fermi mom. More stable pairing

  11. New phase : dSC m , dm ≠0 m ,dm =0 T normal normal Second order phase transitions (MFA) CFL 2SC dSC mCFL

  12. elementary excitation spectra • Gluons • Quasi fermions • (Nambu-Goldstone bosons) ●Gluons (Meissner masses)

  13. e e Unpaired case Paired case p p ● Gapless quasi-fermions Cf. Alford, Berges & Rajagopal (`99), M.Huang & I.Shovkovy (`03) normal phase T mCFL dSC 2SC unpaired 0 0 2 2 5 5 9 paired 0 2 1 3 0 4 0

  14. summary We studied the phase structure near CSC ⇔ QGP boundary with strange quark mass and charge neutrality using Ginzburg-Landau theory m and dm lead to Flavor dependent pF Pairing occur between quarkswith different pF gapless fermion appearsat very close to Tc

  15. thermal phase structure in the mean-field approx. (MFA) & new dSC phase (this work) T Order of the phase transition may change. (beyond MFA) Matsuura, Iida, Hatsuda, and Baym, PRD 074012(2004) QGP 2SC dSC mCFL Hadron gCFL,g2SC, uSC,CFLK,FFLO, BEC,・・・ μ

  16. back up

  17. k k Meissner mass Ginzburg-Landau (T ~Tc) local coupling to gluons mA2 >0 (always) QCD nonlocal coupling to gluons δ > 0.3041 ×2πkB T mA82 , κ < 0 unstable to FFLO δ < 0.3041 ×2πkB T ← our case mA82 , κ > 0 stable to FFLO 2δ κ:momentum susceptibility Giannakis & Ren (hep-ph/0412015)

  18. Why color neutrality does not play role ? T μe normal Tc μe,μ8 super μ8

  19. “BCS”pairing(zero free energy condition) F=E-μN FFLOpairing μu <μd ku=q + pkd=q – p

  20. Δ~σTc dT μ ~σTc Order of Δ and δT Effect of Fluctuation ⇒ dT ~ g2 Tc or gTc>>σTc(at high density)

  21. T ~0 vs T ~Tc P A δ<< Tc B C T ~0 difference is important T ~Tc average is important

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