Model identification in ${\mu }^{-}\to e^{-}$ conversion with invisible boson emission using muonic atoms

In this article, we investigate the ${\mu }^{-}\to e^{-}X$ process in a muonic atom, where $X$ is a light neutral boson. By calculating the spectrum of the emitted electron for several cases, we discuss the model-discriminating power of the process. We report the strong model dependence of the spectrum near a high-energy endpoint. Our findings show that future experiments using muonic atoms are helpful to identify the properties of exotic bosons.