Phase Transition in Dense QCD with the Schwinger-Dyson Equation

We investigate the phase structure of dense QCD using the Schwinger-Dysonequation (SDE) with the improved ladder approximation in the Landau gauge. Weuse the gluon propagator with the electric mode corrected by Debye screeningand the magnetic mode corrected by Landau damping. We solve the coupled SDE forthe Majorana masses of the quark and antiquark (separately from the SDE for theDirac mass) in the low density and intermediate density regions. In the lowdensity region, both the SDEs for the Majorana masses and the Dirac mass havenontrivial solutions that correspond to the color symmetry breaking (CSB)vacuum and the chiral symmetry breaking ($\chi$SB) vacuum. Comparing the valuesof the effective potential in the two vacua, we show that the phase transitionfrom the $\chi$SB vacuum to the CSB vacuum is of first order. The resultantvalue of the critical chemical potential is about 210 MeV, which is smallerthan that obtained from the SDE analysis including only the Dirac mass. Themomentum dependences of the Majorana masses of the quark and antiquark areshown to be quite different, although the masses are of the same order.Comment: 37 pages, 18 figures, 3 figures and references adde