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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 theoryfor two-body decays of $S$ into SM particles. We explicitly compute the Wilsoncoefficients of the SCET$_{\rm BSM}$ operators appearing at leading andnext-to-leading order (NLO) in an expansion in powers of $v/M_S$, as well asfor a subset of operators arising at NNLO, retaining the full dependence on theratio $M_S/M_\Psi$. For the phenomenologically most relevant decay channels ofthe heavy scalar, we study the impact of resummation effects of Sudakovlogarithms on the decay rates.

Effective Theory for a Heavy Scalar Coupled to the SM via Vector-Like Quarks