Superconducting phase transition in the Nambu - Jona-Lasinio model

The Nambu - Bogoliubov - de Gennes method is applied to the problem of superconducting QCD. The effective quark-quark interaction is described within the framework of the Nambu - Jona-Lasinio model. The details of the phase diagram are given as a function of the strength of the quark-quark coupling constant $G^{\mathrm{\prime }}$. It is find that there is no superconducting phase transition when one uses the relation between the coupling constants $G^{\mathrm{\prime }}$ and $G$ of the Nambu - Jona-Lasinio model which follows from the Fierz transformation. However, for other values of $G^{\mathrm{\prime }}$ one can find a rich phase structure containing both the chiral and the superconducting phase transitions.