  Quantum interactions exchanging different types of particles play a pivotal
r\^{o}le in quantum many-body theory, but they are not sufficiently
investigated from a mathematical perspective. Here, we consider a system made
of two fermions and one boson, in order to study the effect of such an
off-diagonal interaction term, having in mind the physics of cuprate
superconductors. Additionally, our model also includes a generalized Hubbard
interaction (i.e., a general local repulsion term for the fermions). Regarding
pairing, exponentially localized dressed bound fermion pairs are shown to exist
and their effective dispersion relation is studied in detail. Scattering
properties of the system are derived for two channels: the unbound and bound
pair channels. We give particular attention to the regime of very large on-site
(Hubbard) repulsions, because this situation is relevant for cuprate
superconductors.
