Searching for new physics at $\mu \to e$ facilities with ${\mu }^{+}$ and ${\pi }^{+}$ decays at rest

We investigate the ability of $\mu \to e$ facilities, Mu2e and COMET, to probe, or discover, new physics with their detector validation datasets. The validation of the detector response may be performed using a dedicated run with ${\mu }^{+}$, collecting data below the Michel edge, $E_e\lesssim 52$ MeV; an alternative strategy using ${\pi }^{+}\to e^{+}{\nu }_e$ may also be considered. We focus primarily on a search for a monoenergetic $e^{+}$ produced via two-body decays ${\mu }^{+}\to e^{+}X$ or ${\pi }^{+}\to e^{+}X$, with $X$ a light new physics particle. Mu2e can potentially explore new parameter space beyond present astrophysical and laboratory constraints for a set of well motivated models including: axion like particles with flavor violating couplings (${\mu }^{+}\to e^{+}a$), massive $Z^{\mathrm{\prime }}$ bosons (${\mu }^{+}\to Z^{\mathrm{\prime }}{e}^{+}$), and heavy neutral leptons (${\pi }^{+}\to e^{+}N$). The projected sensitivities presented herein can be achieved in a matter of days.