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

We investigate the ability of $\mu\rightarrow e$ 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 $\pi^+\rightarrow e^+ \nu_e$ may also be considered. We focus primarily on a search for a monoenergetic $e^+$ produced via two-body decays $\mu^+ \rightarrow e^+ X$ or $\pi^+\rightarrow e^+X$, 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 ($\mu^+ \rightarrow e^+ a$), massive $Z'$ bosons ($\mu^+ \rightarrow Z' e^+$), and heavy neutral leptons ($\pi^+\rightarrow e^+N$). The projected sensitivities presented herein can be achieved in a matter of days.