A study of diquark and meson condensation in the Nambu–Jona-Lasinio model and Fermi momentum

Using a three- and four-dimensional Pauli–Villars regularization scheme, we investigate quark–antiquark and diquark condensation in the framework of the Nambu–Jona-Lasinio model. Using the particle Fermi momentum as a cutoff parameter, we study the energy gap width and coherence length for the meson condensate $\langle q\bar q\rangle$. We also study the energy gap width and critical coherence length (the distance over which there would be no diquark condensation) for the diquark $\langle qq\rangle$ and the dependence on the Fermi momentum. We obtain an estimate of the Fermi momentum value for meson and diquark condensates with an energy gap width of the order of $100$ MeV.