IRGAC 2006 COLOR SUPERCONDUCTIVITY and MAGNETIC FIELD: Strange Bed Fellows in the Core of Neutron Stars? Vivian de la Incera Western Illinois University Barcelona, Spain, July 11-15, 2006

IRGAC 2006 B~ – G in the surface of pulsars B~ – G in the surface of magnetars Neutron Stars Diameter: Mass: Magnetic fields: Density:

Color Superconductivity Magnetic Field and Color Superconductivity MCFL: Symmetry, gap structure, gap solutions Conclusions and Outlook E.J. Ferrer, V.I. and C. Manuel, PRL 95, ; NPB 747, 88. IRGAC 2006 Outline

IRGAC 2006 Color Superconductivity Bailin and Love ‘84

IRGAC 2006 Three flavors at very high density: CFL phase Pairs: spin zero, antisymmetric in flavor and color Rapp, Schafer, Shuryak and Velkovsky, ‘98 Alford, Rajagopal and Wilczek, ‘98

Magnetic Field Inside a Color Superconductor In spin-zero color superconductivity a linear combination of the photon and one gluon remains massless (in-medium electromagnetic field). An external magnetic field penetrates the superconductor in the form of a “rotated” field (no Meissner effect) uuudddsss CHARGES All -charged quarks have integer chargesAll pairs are -neutral IRGAC 2006

Color Superconductivity & B Will a magnetic field reinforce color superconductivity?

CFL: SU(3) C X SU(3) L X SU(3) R X U(1) B X U(1) e.m. SU(3) C+L+R X U(1) e.m Rapp, Schafer, Shuryak and Velkovsky, PRL 81 (1998) Alford, Rajagopal and Wilczek, PLB 422 (1998) MCFL: SU(3) C X SU(2) L X SU(2) R X U(1) B X U(1) e.m X U (-) (1) A SU(2) C+L+R X U(1) e.m Ferrer, V.I. and Manuel PRL 95, Dominant attractive interactions in 3-flavor QCD lead to a general order parameter of the form IRGAC 2006 B = 0 B 0

Three-flavor NJL Theory with Rotated Magnetic Field

MCFL ansatz including subdominant interactions only get contributions from pairs of neutral quarks IRGAC 2006 get contributions from pairs of neutral and pairs of charged quarks

where the Gorkov fields are defined by: The mean-field action can be written as: and the Gorkov inverse propagators are IRGAC 2006

Gap Equations IRGAC 2006

For fields the gap equations can be reduced to IRGAC 2006

Gap Solutions Ferrer, V.I. and Manuel, NPB 747, 88 IRGAC 2006

 The magnetic field “helps” CS. The field reinforces the gap that gets contributions from pairs of -charged quarks.  The physics behind MCFL is different from the phenomenon of magnetic catalysis. In MCFL the field reinforces the diquark condensate through the modification of the density of state

CFL vs MCFL 9 Goldstone modes: charged and neutral. 5 Goldstone modes: all neutral Low energy similar to low density QCD. Schafer & Wilzcek’ PRL 82 (1999) Low energy similar to low density QCD in a magnetic field. Ferrer, VI and Manuel, NPB’06 IRGAC 2006

CONCLUSIONS and OUTLOOK  Neutron stars provide a natural lab to explore the effects of B in CS  Is MCFL the correct state at intermediate, more realistic, magnetic fields? Gluon condensates?  What is the correct ground state at intermediate densities; is it affected by the star’s magnetic field?  Explore possible signatures of the CS-in-B phase in neutron stars: neutrino cooling, thermal conductivity, etc. IRGAC 2006