Searching for the dark sector in two-body antimuon decay with the polarization of monochromatic positrons

The $\mu^+ \to e^+ X$ decay, where $X$ is a dark sector boson, provides one of the strongest available bounds on the scale of dark sector interactions. The boson $X$ can be an axion or a dark photon. A measure of the polarization of the positron can help in controlling the Standard Model background in the search for a signal and, assuming that a signal is seen, make possible to distinguish with a confidence level of 99% the spin--0 or 1--of the dark sector boson with as few as 6 events in the case of the massless dark photon and 9 in the massive case. We also discuss the possibility that the boson $X$ be a massive spin-2 particle.