Minkowski space approach for the Bethe-Salpeter equation

Abstract

The bound-state energy spectrum for two-boson system with a fixed exchanged massive boson is investigated by considering the scalar Bethe-Salpeter (BS) equation in Minkowski space within the ladder-Approximation framework. The approach is extending to excited states a previous study performed for the ground state. The number of states in the spectrum is restricted by the coupling strength of the two-body interaction, as well as the mass of the exchanged boson. In the present approach, we use the Nakanishi Integral Representation and the formally exact null-plane projection. As usual a comparison between eigenvalues obtained in the Minkowski and Euclidean space is presented. Within such scheme, the light-front momentum-space valence wave functions are obtained for the ground and excited states, together with the corresponding quantities in the impactparameter space. Among relevant features emerging from this study, we can point out the node structure of light-front wave function and the leading exponential fall-off of the valence wave function in the impact-parameter space.