Structural change of Cooper pairs and momentum-dependent gap in color superconductivity

Abstract

The two-flavor color superconductivity is studied over a wide range of baryon density with a single model. We pay special attention to the spatial-momentum dependence of the gap and to the spatial structure of Cooper pairs. At an extremely high baryon density $[\ensuremath{\sim}\mathcal{O}{(10}^{10}{\ensuremath{\rho}}_{0})$ with ${\ensuremath{\rho}}_{0}$ being the normal nuclear matter density], our model becomes equivalent to the usual perturbative QCD treatment and the gap is shown to have a sharp peak near the Fermi surface due to the weak-coupling nature of QCD. On the other hand, the gap is a smooth function of momentum at lower densities $[\ensuremath{\sim}\mathcal{O}(10{\ensuremath{\rho}}_{0})]$ due to strong color magnetic and electric interactions. To study the structural change of Cooper pairs from high density to lower density, the quark correlation in the color superconductor is studied both in momentum space and in coordinate space. The size of the Cooper pair is shown to become comparable to the averaged interquark distance at low densities. Also, the effects of the momentum-dependent running coupling and the antiquark pairing, which are both small at high density, are shown to be non-negligible at low densities. These features are highly contrasted to the standard BCS superconductivity in metals.