  The ladder Bethe-Salpeter Equation of a bound (1/2)+ system, composed by a
fermion and a scalar boson, is solved in Minkowski space, for the first time.
The formal tools are the same already successfully adopted for two-scalar and
two-fermion systems, namely the Nakanishi integral representation of the
Bethe-Salpeter amplitude and the light-front projection of the fulfilled
equation. Numerical results are presented and discussed for two interaction
kernels: i) a massive scalar exchange and ii) a massive vector exchange,
illustrating both the correlation between binding energies and the interaction
coupling constants, as well as the valence content of the interacting state,
through the valence probabilities and the light-front momentum distributions.
In the case of the scalar exchange, an interesting side effect, to be ascribed
to the repulsion generated by the small components of the Dirac spinor, is
pointed out, while for the vector exchange the manifestation of the helicity
conservation opens new interesting questions to be addressed within a fully
non-perturbative framework, as well as the onset of a scale-invariant regime.
