  Obtaining precise theoretical predictions for both production and decay
processes of heavy new particles is of great importance to constrain the
allowed parameter spaces of Beyond-the-Standard-Model (BSM) theories, and to
properly assess the sensitivity for discoveries and for discriminating between
different possible BSM scenarios. In this context, it is well known that large
logarithmic corrections can appear in the presence of widely separated mass
scales. We point out the existence of a new type of possible large,
Sudakov-like, logarithms in external-leg corrections of heavy scalars. To the
difference of usual Sudakov logarithms, these can furthermore potentially be
enhanced by large trilinear couplings. Such large logarithms are associated
with infrared singularities and we review several techniques to address these
at one loop. In addition to this discussion, we also present the derivation of
the two-loop corrections containing this type of large logarithms, pointing out
in this context the importance of adopting an on-shell renormalisation scheme.
Finally, we illustrate our calculations and examine the possible magnitude of
these corrections for a simple scalar toy model as well as for decay processes
involving heavy stop quarks in the Minimal Supersymmetric Standard Model and a
heavy Higgs boson in the Next-to-Two-Higgs-Doublet Model.
