Color Superconductivity in the Schwinger-Dyson Approach: Strange Quark Mass and the 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 the antiquark contribution to the pairing gap due to the large effective coupling, cause the gap, critical temperature and their ratio to deviate from the weak coupling values. Nevertheless, the ratio of the physical quantity for the CFL state and that for the 2SC state does not differ so much from the weak coupling value, as long as the pairing interaction is taken to be the same for both cases. As a consequence, the CFL state always dominates the 2SC state and the critical temperatures of the transitions to the quark-gluon plasma (QGP) phase from both states coincide in the chiral limit. The energy gain in the CFL state relative to the 2SC state becomes smaller as the critical line dividing (μ, T) plane into the QGP and CFL phases is approached, and thus small perturbations can lift the degeneracy of these critical lines. As one of the perturbations, the effect of the strange quark mass ms on the quark-pairing is examined. In particular, using a simple kinematical criterion, we discuss the behavior of the ‘ color-flavor unlocking line’, on which the CFL phase turns into the 2SC phase, through the variation of ms.