Formation of gapless phases of K0 condensed color-flavor locked superconducting quark matter

Electric and color neutral solutions, and the critical conditions for the formation of gapless color superconductors, are investigated in K-0 condensed color-flavor locked quark matter for nonzero strange quark mass. We show that as the strange quark mass increases, gapless modes for up-strange quark pairing occur first, followed by down-strange quark pairing. The behavior of the gaps, the dispersion relations, and the thermodynamic potential are all found as functions of the strange quark mass on the basis of a Nambu-Jona-Lasinio type model. To a high degree of accuracy, they are presented as relatively simple elementary functions. This allows for easy computation for any reasonable range of baryon chemical potential and strange quark mass.