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.