Color Superconductivity in Schwinger-Dyson Approach -- Strange Quark Mass and Color-Flavor Unlocking Line --

Abstract

Phase structure and phase transitions in dense QCD are studied using the Schwinger-Dyson (SD) method in the improved ladder approximation. We construct the Cornwall-Jackiw-Tomboulis (CJT) effective potentials at finite temperature for two types of pairing ansatz, namely the Color-Flavor locking (CFL) state and the two flavor superconducting (2SC) state. Strong coupling effects at low densities, such as the off-Fermi surface and antiquarks contribution to the pairing gap due to the large effective coupling, make the gap, critical temperature and those ratio deviate from those weak coupling values. Nevertheless, the ratio of the physical quantity for the CFL and that for the 2SC does not differ so much from the weak coupling value, as long as the pairing interaction is taken to be the same for the both cases. As a consequence, the CFL state always dominates over 2SC state and the critical temperatures to quark-gluon plasma (QGP) from both states coincides in the chiral limit. The energy gain in the CFL state relative to the 2SC state gets smaller towards the critical line dividing (mu, T) plane into the QGP and CFL phases, and thus small perturbations can remove the degeneracy of these critical lines. As one of such perturbations, the effect of the strange quark mass m_s on the quark-pairing is examined. In particular, using a simple kinematical criterion, we discuss the behaviour of the ``color-flavor unlocking line'' on which the CFL phase turns into the 2SC phase, against the variation of m_s.