  Perturbative calculations for processes that involve heavy flavours can be
performed in two approaches: the massive scheme and the massless one. The
former enables one to fully account for the heavy-quark kinematics, while the
latter allows one to resum potentially-large mass logarithms. Furthermore, the
two schemes can be combined to take advantage of the virtues of each of them.
Both massive and massless calculations can be supplemented by soft-gluon
resummation. However matching between massive and massless resummed
calculations is difficult, essentially because of the non-commutativity of the
soft and massless limits. In this paper, we develop a formalism to combine
resummed massless and massive calculations. We obtain an all-order expression
that consistently resums both mass and soft logarithms to next-to-leading
logarithmic accuracy. We perform detailed calculations for the decay of the
Higgs into a heavy-quark pair and discuss the applications of this formalism to
different processes.
