  We illustrate the application of the recently developed SCET$_{\rm BSM}$
framework in the context of a specific model, in which the Standard Model (SM)
is supplemented by a heavy scalar $S$ and three generations of heavy,
vector-like quarks $\Psi$. We construct the appropriate effective field theory
for two-body decays of $S$ into SM particles. We explicitly compute the Wilson
coefficients of the SCET$_{\rm BSM}$ operators appearing at leading and
next-to-leading order (NLO) in an expansion in powers of $v/M_S$, as well as
for a subset of operators arising at NNLO, retaining the full dependence on the
ratio $M_S/M_\Psi$. For the phenomenologically most relevant decay channels of
the heavy scalar, we study the impact of resummation effects of Sudakov
logarithms on the decay rates.
