  In this study, we introduce a parametric function designed to describe the
energy distribution of the observed particle within the framework of two-body
decays involving one undetected particle, analyzed using the pseudo-rest frame
approximation. While we illustrate its effectiveness through the specific case
study of the Lepton Flavor Violating decay $\tau \rightarrow l+\alpha$, this
parametric function is broadly applicable to a wide range of pseudo-rest frame
method-related searches involving undetected particles. Remarkably, it requires
only a single simulation to account for the smearing effects resulting from the
pseudo-rest frame approximation. The uniqueness of this function lies in its
dependency on the mass of the undetected particle, enabling continuous
exploration of the mass parameter space. We validate the performance of our
parametric function using simulated datasets and find that it exhibits
comparable performance to traditional simulation-based methods. Notably, our
approach offers the distinct advantage of accommodating any mass value for the
undetected particle without the need for multiple simulations.
