  Relations between multiple unitarity cuts and coproducts of Feynman integrals
are extended to allow for internal masses. These masses introduce new branch
cuts, whose discontinuities can be derived by placing single propagators on
shell and identified as particular entries of the coproduct. First entries of
the coproduct are then seen to include mass invariants alone, as well as
threshold corrections for external momentum channels. As in the massless case,
the original integral can possibly be recovered from its cuts by starting with
the known part of the coproduct and imposing integrability contraints. We
formulate precise rules for cuts of diagrams, and we gather evidence for the
relations to coproducts through a detailed study of one-loop triangle integrals
with various combinations of external and internal masses.
