  We use the point-particle effective field theory (PPEFT) framework to
describe particle-conversion mediated by a flavour-changing coupling to a
point-particle. We do this for a toy model of two non-relativistic scalars
coupled to the same point-particle, on which there is a flavour-violating
coupling. It is found that the point-particle couplings all must be
renormalized with respect to a radial cut-off near the origin, and it is an
invariant of the flow of the flavour-changing coupling that is directly related
to particle-changing cross-sections. At the same time, we find an interesting
dependence of those cross-sections on the ratio k_out/k_in of the outgoing and
incoming momenta, which can lead to a 1/k_in enhancement in certain regimes. We
further connect this model to the case of a single-particle non-self-adjoint
(absorptive) PPEFT, as well as to a PPEFT of a single particle coupled to a
two-state nucleus. These results could be relevant for future calculations of
any more complicated reactions, such as nucleus-induced electron-muon
conversions, monopole catalysis of baryon number violation, as well as nuclear
transfer reactions.
