Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space

Abstract

The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz or assumption. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is found.

Comments: 10 pages, 2 figures, version accepted for publication in Phys. Lett. B