Diquark condensation and the quark-quark interaction

We employ a bispinor gap equation to study superfluidity at nonzero chemical potential, $\mu \ne 0,$ in two- and three-color QCD, exploring the gap’s sensitivity to the nature of the quark-quark interaction. The two-color theory, ${\mathrm{QC}}_2\mathrm{D},$ is an excellent exemplar; the order of truncation of the quark-quark scattering kernel K has no qualitative impact, which allows a straightforward elucidation of the effects of $\mu$ when the coupling is strong. In the three-color theory the rainbow-ladder truncation admits diquark bound states, a defect that is eliminated by an improvement of K. The corrected gap equation describes a superfluid phase that is semiquantitatively similar to that obtained using the rainbow truncation. A model study suggests that the width of the superfluid gap and the transition point in ${\mathrm{QC}}_2\mathrm{D}$ provide reliable quantitative estimates of those quantities in QCD.