  Recently, formalism has been derived for studying electroweak transition
amplitudes for three-body systems both in infinite and finite volumes. The
formalism provides exact relations that the infinite-volume amplitudes must
satisfy, as well as a relationship between physical amplitudes and
finite-volume matrix elements, which can be constrained from lattice QCD
calculations. This formalism poses additional challenges when compared with the
analogous well-studied two-body equivalent one, including the necessary step of
solving integral equations of singular functions. In this work, we provide some
non-trivial analytical and numerical tests on the aforementioned formalism. In
particular, we consider a case where the three-particle system can have
three-body bound states as well as bound states in the two-body subsystem. For
kinematics below the three-body threshold, we demonstrate that the scattering
amplitudes satisfy unitarity. We also check that for these kinematics the
finite-volume matrix elements are accurately described by the formalism for
two-body systems up to exponentially suppressed corrections. Finally, we verify
that in the case of the three-body bound state, the finite-volume matrix
element is equal to the infinite-volume coupling of the bound state, up to
exponentially suppressed errors.
