Aspects of the color flavor locking phase of QCD in the Nambu-Jona-Lasinio approximation

We study two aspects of the color flavor locked phase of QCD in the Nambu-Jona-Lasinio approximation. The first one is the issue of the dependence on mu of the ultraviolet cutoff in the gap equation, which is solved by allowing for a running coupling constant. The second one is the dependence of the gap on the strange quark mass; using high density effective theory we perform an expansion in the parameter (m(s)/mu)(2) after checking that its numerical validity is already very good at first order.