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Thermal unpairing transitions affected by charge neutrality constraints and chiral dynamics

Thermal unpairing transitions affected by charge neutrality constraints and chiral dynamics. Hiroaki Abuki in collaboration with Teiji Kunihiro (Yukawa Institute of Kyoto Univ., JAPAN) Based on arXiv:hep-ph/0509172. Color superconductivity. Rich variety of phase candidates.

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Thermal unpairing transitions affected by charge neutrality constraints and chiral dynamics

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  1. Thermal unpairing transitionsaffected by charge neutrality constraints and chiral dynamics Hiroaki Abuki in collaboration with Teiji Kunihiro (Yukawa Institute of Kyoto Univ., JAPAN) Based on arXiv:hep-ph/0509172

  2. Color superconductivity • Rich variety of phase candidates dsusudJP=0+ dsusud • Possible States # of gapped quasi-quarks • CFL (9)D1 = D2 = D39(all quarks) • 2SC (4)D3 0 ( udpair ) 4 • dSC (6)? D2= 0 ( withoutds pair ) 6 Alford-Rajagopal-Wilczek (’98) Bailin-Love (84), Iwasaki-Iwado (’95) Iida-Matsuura-Tachiabana-Hatsuda (’04) H. Abuki @ PANIC05, Santa Fe

  3. Various BCS and non-BCS states • Gapless (quasi-)quarks u dsud usds Qtilde = (0, 0, 0) (1, -1) (1, -1) (0, 0) CFL (9) : gCFL (7) : 2SC (4) : g2SC (2) : dSC (6) : gdSC (5) : etc… fullygapped BCS state:Qtilde-insulator us* ds* susds du*sdu*usds su*us su*usds* Alford-Kouvaris-Rajagopal (’03) Shovkovy-Huang, PLB564, 205 (’03) H. Abuki @ PANIC05, Santa Fe

  4. g2SC(2) Add neutrality constraints and b-equilibrium condition gCFL(7) Effective potential for T = 0, Diquark coupling D0 = 25 [MeV] Only direct effect of strange quark mass 1st order CFL 2SC Alford-Berges-Rajagopal, ’99 Schaefer-Wilczek, ’99 Unpaired(0) Alford-Rajagopal, ’02 Continuous CFL gCFL 1st ordergCFL  UQ 2SC(4) CFL(9) Alford-Kouvaris-Rajagopal, ’03 high density low density

  5. Dynamical effects? • Chiral dynamics in scalar qqbar channel • Strong coupling effects beyond MFA Strange quark mass is NOT an external parameter like magnetic field applied to metallic superconductor! Ms is dynamical variable and is phase-dependent Abuki-Kitazawa-Kunihiro, PLB615, 102 (2005) Ruster et al.,PRD72, 034004 (2005) Blaschke et al., PRD72, 065020 (2005) Abuki-Kunihiro, arXiv:hep-ph/0509172 Interplay between the dynamical and kinetic effects Just neglect this effect in this talk; BCS-BEC crossover scenario Nishida-Abuki, arXiv:hep-ph/0504083  poster Precursory fluctuation Kitazawa-Koide-Nemoto-Kunihiro, PRD65, 091504 (2002) H. Abuki @ PANIC05, Santa Fe

  6. : (qq) attraction in QCD brings about superconductivity : (qqbar) attraction in QCD causes the CSB at low density determined by neutrality constraints A four-Fermi model Start with Extended NJL model Condensate ansatz

  7. Extremely small Gd[D0] Intermediate Gd[D0] Small Gd[D0] Gapless CFL Phase diagram for various Gd Extremely weak coupling uSC  gCFLCFL Weak coupling uSC  UQMCFL Moderate coupling uSC  2SC CFL

  8. Why dSC phase does not appear? • This seemingly contradicts the claim ｂｙ • But consistent with the results in • Where this discrepancy comes from?? Ginzburg-Landau analysis with Ms as a parameter Iida-Matsuura-Tachibana-Hatsuda, PRL93, 132001 (2004) NJL numerical anslysis with Ms as a dynamical variable Ruster et al., PRD72, 034004 (2005) Blaschke et al., PRD72, 065020 (2005) The answer is given by our recent work: Abuki-Kunihiro, arXiv:hep-ph/0509172 aimed at the unified description of thermal transitions H. Abuki @ PANIC05, Santa Fe

  9. O(Ms2) splitting in Tc O(Ms4) splitting in Tc Iida et al. (’04) Abuki-Kunihiro. (’05) Ginzburg-Landau re-analysis Effect of strange quark mass and neutrality condition Free fermi gas part Usual GL part Iida-Baym (’01) By solving min.{b-1a} = 0, one gets the critical temperature for CFL non-CFL H. Abuki @ PANIC05, Santa Fe

  10. stress energy [MeV]D0 stress energy [MeV]D0 1 6 1 6 7 T/Tc0 T/Tc0 CFL uSC appears at low density: Fukushima et al, ’03 high density low density Doubly critical point (DCP): first noticed in the NJL study by Fukushima-Kouvaris-Rajagopal (’04) Abuki-Kunihiro ’05 Ginzburg-Landau re-analysis uQM uQM dSC 2SC 2SC dSC CFL uSC dSC as second coldest phase : Iida et al (2003) Growing window for dSC at high density

  11. Ginzburg-Landau re-analysis In the weak coupling perturbative regime • If (Ms<<D0), then the dSC will be realized • If (Ms>>D0), then the uSC will be realized • Ms is a decreasing function of m • D0 is an increasing function of m Ms  ms 100MeV while D0>100MeV only for m >1011 MeV c.f. Schaefer-Wilczek, PRD60, 114033 (1999)

  12. Summary • Extensive analysis of the phase diagram • The second densest phase depends on the strength of the (qq)-coupling • The second coldest phase depends on quark density • Analytic nature of the DCP was clarified Please see Abuki-Kunihiro, arxiv:hep-ph/0509172 for more details Interplay with chiral dynamics; gCFL, uQM, g2SC or 2SC? Abuki-Kitazawa-Kunihiro, PLB615, 102 (2005) dSC at high density, or uSC at low density dSC is realized at extremely high density in QCD H. Abuki @ PANIC05, Santa Fe

  13. Future issues • Instability in the gapless phases? • Seek for astrophysical consequences Crystalline ordered phase?? Alford-Bowers-Rajagopal, PRD63, 074016 (2001) Casalbuoni et al., arXiv:hep-ph/0507247, …etc. Gluonic phase?? Gorbar-Hashimoto-Miransky, arXiv:hep-ph/0507303. Anything other?? Bulk structure of NS Neutrino transport property and NS Cooling Viscosity and R-mode instability etc. H. Abuki @ PANIC05, Santa Fe

  14. LOFF phase? From Casalbuoni et al., arXiv:hep-ph/0507247 LOFF line was calculated within the Ginzburg-Landau approach We still have a wide unstable region! Needs something further H. Abuki @ PANIC05, Santa Fe

  15. Backup slides • Ginzburg-Landau potential up to quartic order • Why the gCFL is taken over at strong coupling? • Phase diagram for even stronger coupling • Phases for extremely weak coupling • Cutting phase diagram for T=0 • Cutting phase diagram for finite T • Phases for Weak coupling • Cutting phase diagram at finite T • Why the g2SC phase at finite T? • Phases for Intermediate coupling • Cutting phase diagram at finite T • Why the g2SC phase at finite T? • Baryon number density vs. m H. Abuki @ PANIC05, Santa Fe

  16. Trajectory of gCFL onset point m*  line of UQM energy gain is huge due to large Second densest phase and Gd • Why the gCFL ceases to be second phase? UQM without <qqbar> D0 = 0

  17. Abuki-Kunihiro ’05 Ginzburg-Landau re-analysis

  18. g2SC(2) gCFL(7) Add neutrality constraints and b-equilibrium condition Effective potential from a model Only direct effect of strange quark mass 1st order unlocking CFL 2SC Unpaired(0) 2SC(4) continuous transition CFL gCFL 1st order gCFL  UQ Alford-Berges-Rajagopal, ’99 Schaefer-Wilczek, ’99 Alford-Rajagopal, ’02 CFL(9) Alford-Kouvaris-Rajagopal, ’03 high density low density

  19. Even stronger coupling Extremely weak coupling uSC  2SCCFL

  20. Extremely weak coupling

  21. Cutting phase diagram Quark densities: Enforced neutrality in CFL phase Gap parameters and chemical potentials Gaps in quark spectra: SU(2)C+Vsymmetry CFL / gCFL  Kaon cond.

  22. Extremely weak coupling

  23. Cutting phase diagram Gap parameters and chemical potentials Gaps in quark spectra behave in more complicated manner! metal / insulator crossover: gCFL8 / CFL

  24. Weak coupling

  25. Cutting phase diagram Gap parameters and chemical potentials

  26. Why the g2SC phase at finite T? We needs close look at the structure of the uQM solution which would be unstable against pair formation only at finite T

  27. Why the g2SC phase at finite T? Occupation number for u and d quarks Isospin mismatch is reduced at finite T due to thermal effect Instability to formation of Iso-singlet qq

  28. Intermediate coupling Unusual 1st order 2SC / g2SC Transition What is happening in the 2SC sector?

  29. Cutting phase diagram Gap parameters and chemical Potentials in the 2SC sector 1st order 2SC / g2SC transition Neutral Isospin density Order parameter for 2SC/g2SC

  30. Intermediate coupling

  31. Cutting phase diagram Gap parameters and chemical Potentials in the 2SC sector Neutral Isospin density Smooth crossover 2SC / g2SC

  32. Baryon number density Several jumps at 1st order transitions Baryon density in the CFL Increases with coupling O( D2/m2 ) Minimum CFL density decreases however

  33. Dense phase of QCD • The most prominent candidate of Densest / Coldest phase: Color-Favor Locking (CFL) • What’s the 2nd densest phase? Alford-Rajagopal-Wilczek, NPB537:443 (1999) Schaefer, NPB575, 269 (2000)) But only convincing for mMs • Strange quark mass • Charge neutrality constraints & b-equilibrium condition Alford-Berges-Rajagopal, NPB558, 219 (1999) Schaefer-Wilczek, PRD60, 074014 (1999) Iida-Baym, PRD63, 074018 (2001) Rajagopal-Wilczek, PRL86, 3492 (2001) Amore-Birse-McGovern-Walet, PRD65, 074005 (2002) Alford-Rajagopal, JHEP0206, 031 (2002) Alford-Kouvaris-Rajagopal, PRL92, 222001 (2004)

  34. T CSC m Hadrons Strong coupling dynamical effects? Dynamical effects? • Chiral dynamics in scalar qqbar channel Strange quark mass is NOT an external parameter Abuki-Kitazawa-Kunihiro, PLB615, 102 (2005) Ruster et al.,PRD72, 034004 (2005) Blaschke et al., PRD72, 065020 (2005) Abuki-Kunihiro, arXiv:hep-ph/0509172 Nonlinear Interplay between dynamical and kinetic effects H. Abuki @ PANIC05, Santa Fe

  35. Setting model (2) • Parameter settings • Chiral SU(2) limit: • mu= md= 0, and mu = 80 MeV • (q-qbar) coupling • set Gsso thatMu,d =400MeV atm=0 • (q-q) coupling • treat Gd simply as a parameter: • Gd D0 (one to one correspondence H. Abuki @ PANIC05, Santa Fe

  36. Ginzburg-Landau analysis Effective potential can be expanded in D1,2,3 near Tc For symmetric matter at extremely high density c.f. Iida-Baym, PRD63, 074018 (2001) Giannakis-Ren, PRD65, 054017 (2002) Three equal temperature: Simultaneous melting at Tc0 H. Abuki @ PANIC05, Santa Fe

  37. O(Ms2) splitting in Tc O(Ms4) splitting in Tc a1was first calculated in Iida et al., PRL93, 132001 (2004) me/3 s Ms Ms + s d s d By solving min.{b-1a} = 0, one gets the critical temperature for CFL non-CFL D1 D1* D3 D3* d u Ginzburg-Landau re-analysis Effect of strange quark mass and neutrality condition Free fermi gas part! Usual GL part H. Abuki @ PANIC05, Santa Fe

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