  We describe a generalization of the Lellouch-L\"uscher formula to the case of
multiple strongly-coupled decay channels. As in the original formula, our final
result is a relation between weak matrix elements in finite and infinite
volumes. Our extension is limited to final states with two scalar particles,
with center of mass energies below the lowest three- or four-particle
threshold. Otherwise the extension is general, accommodating any number of
channels, arbitrary strong coupling between channels, as well as any form of
weak decay operators in the matrix elements. Among many possible applications,
we emphasize that this is a necessary first step on the way to a lattice-QCD
calculation of weak decay rates for D -> pi pi and D -> K K-bar. Our results
allow for arbitrary total momentum and hold for degenerate or non-degenerate
particles.

High Energy Physics - Lattice