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The Single Flavor Color Superconductivity in a Magnetic Field

The Single Flavor Color Superconductivity in a Magnetic Field. Bo Feng De-fu Hou Hai-cang Ren Ping-ping Wu Institute of particle physics ,CCNU. Phys. Rev. Lett. 105, 042001 (2010). Motivation to study single flavor CSC Ground state for single flavor CSC

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The Single Flavor Color Superconductivity in a Magnetic Field

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  1. The Single Flavor Color Superconductivity in a Magnetic Field Bo Feng De-fu Hou Hai-cang Ren Ping-ping Wu Institute of particle physics ,CCNU Phys. Rev. Lett. 105, 042001 (2010)

  2. Motivation to study single flavor CSC Ground state for single flavor CSC Ground state for single flavor CSC in a magnetic field Conclusion and outlook Outlines

  3. QCD at arbitrarily high density • No reliable lattice results at finite density • No reliable effective models of dense QCD • Complications due to charge neutrality and equilibrium • Difficulties in determining stable ground state

  4. Color superconductivity Ground state of dense quark matter • Deconfined quarks( ) • Pauli principle (s=1/2) • Effective models( ) • One-gluon exchange( ) Cooper instability Color superconductivity B. Barrois, NPB 129, 390 (1977) D. Bailin and A. Love, Phys. Rep. 107,325 (1984) M. Alford et al., PLB 422, 247 (1998) R. Rapp et al., PRL 81, 53 (1998)

  5. Phase structure of CSC • BCS type paring: J=0: 2SC: CFL: J=1: • Non-BCStype paring: gaplessphases LOFF …… all quarks participate in the paring M. Alford, K. Rajagopal and F. Wilczek, NPB 537, 443 (1999) :Pairing two quarks with same flavor T. Schaefer, PRD 62, 094007 (2000) A. Schmitt, PRD 71, 054016 (2005) Shovkovy and M. Huang, PLB 546, 205 (2003) M. Alford et al., PRL 92, 222001 (2004) M. Alford et al., PRD 63, 074016 (2001) …….

  6. The single flavor CSC (I) CSC in moderate density: equilibrium: Non-zero strange quark mass: Charge neutrality: Fermi momentum Mismatch Single flavor CSC show up M. Alford et al., Rev. Mod. Phys. 80, 1455 (2008)

  7. spherical mixedphase CSL non-spherical longitudinal and transverse pairing states of polar ,planar ,A phase The single flavor CSC (II) A. Schmitt, PRD 71, 054016 (2005) The most stable phase

  8. Angular momentum mixing The most stable state is the transverse CSL even counting angular momentum mixing. A. Schmitt, PRD 71, 054016 (2005) BF D-f Hou and H-c Ren, NPB 796, 500 (2008); NPB 813, 408 (2009); J Phys. G 36, 045005 (2009); in preparation

  9. Neutron star Webber, astro-ph/0407155

  10. The nonzero strange quark mass The typical density inside a neutron star is about 500MeV A magnetic field is present in a compact star and could reach G in magnitude CSC in a compact star P. Reuter, PRD 74, 105008 (2006) T. Schaefer, PRD 62, 094007 (2000)

  11. Ground state for single flavor CSC In a magnitude field In CSL, there is an electromagnetic Meissner effect. In a nonspherical condensate , the Meissner effect is incomplete.

  12. Given by the solution of the gap equation Only pick up the dominant pairing channel----the transverse pairing, The Hamiltonian given by a NJL-like action in the ultra-relativistic limit: M.Alford and G.Cowan,J.Phys.G.G:32,511-528(2006) The condensate of a diquark operator takes the form: Under mean field approximation: here： 12

  13. Introducing The function is given by: We have and For CSL For polar For A For planar 13

  14. For polar and A For planar is related to the electromagnetic field A and the 8-th component of the color field in the normal phase through a U(1) rotation For polar and A For planar The condensate under U(1) transformation

  15. For normal phase For CSL For i=polar,A,planar The Gibbs free energy density:

  16. By balancing the Gibbs free energy of different phases, we obtain the phase diagram with respect to temperature and magnetic field. • T. Schaefer, PRD 62, 094007 (2000); Phys.Rev.D60,114033(1999) • Schmitt, PRD 71, 054016 (2005) • D.T.Son,Phys.Rev.D59,094019(1999) • R.D.Pisarski et al., Phys.Rev.D61,074017(2000) • W.E.Brown et al., Phys.Rev.D62,054016(2000)

  17. Conclusions and outlooks we have explored the consequences of the incomplete Meissner effect of the nonspherical CSC phase of single flavor pairing. We found that with the increasing magnetic field, the ground state of single flavor CSC is no longer CSL phase, but the phase combination of nonspherical phases. Possible phenomenological implications and the influence of the nonzero strange quark mass for the ground state of single flavor CSC are interesting topics deserving further investigations.

  18. Thanks!

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