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′. It is found that there is no superconducting phase transition when one uses the relation between the coupling constants G′ and G of the Nambu–Jona-Lasinio model which follows from the Fierz transformation. However, for other values of G′ one can find a rich phase structure containing both the chiral and the superconducting phase transitions.