Quantitative studies of the homogeneous Bethe-Salpeter equation in Minkowski space

The Bethe-Salpeter equation for a bound system, composed by two massive scalars exchanging a massive scalar, is quantitatively investigated in ladder approximation, within the Nakanishi integral representation approach. For the S-wave case, numerical solutions with a form inspired by the Nakanishi integral representation are calculated. The needed Nakanishi weight functions are evaluated by solving two different eigenequations, obtained directly from the Bethe-Salpeter equation applying the light-front projection technique. A remarkable agreement, in particular, for the eigenvalues, is achieved, numerically confirming that the Nakanishi uniqueness theorem for the weight functions demonstrated in the context of the perturbative analysis of the multileg transition amplitudes and playing a basic role in suggesting one of the two adopted eigenequations can be extended to a nonperturbative realm. The detailed, quantitative studies are completed by presenting both probabilities and light-front momentum distributions for the valence component of the bound state.