  We perform a model-independent, non-perturbative investigation of two-point
and three-point finite-volume correlation functions in the energy regime where
two-particle states can go on-shell. We study three-point functions involving a
single incoming particle and an outgoing two-particle state, relevant, for
example, for studies of meson decays (e.g., B-to-pi Kll) or meson photo
production (e.g., pi gamma-to-pi pi). We observe that, while the spectrum
solely depends on the on-shell scattering amplitude, the correlation functions
also depend on off-shell amplitudes. The main result of this work is a
generalization of the Lellouch-Luscher formula relating matrix elements of
currents in finite and infinite spatial volumes. We extend that work by
considering a theory with multiple, strongly-coupled channels and by
accommodating external currents which inject arbitrary four-momentum as well as
arbitrary angular momentum. The result is exact up to exponentially suppressed
corrections governed by the pion mass times the box size. We also apply our
master equation to various examples, including the two processes mentioned
above as well as examples where the final state is an admixture of two open
channels.
