Discovering intermediate mass sterile neutrinos through $\tau^- \to \pi^- \mu^- e^+ \nu$ (or $\bar{\nu}$) decay

Distinguishing the Dirac and Majorana nature of neutrinos remains one of the most important tasks in neutrino physics. By assuming that the $\tau^- \to \pi^- \mu^- e^+ \nu$ (or $\bar{\nu}$) decay is resonantly enhanced by the exchange of an intermediate mass sterile neutrino $N$, we show that the energy spectrum of emitted pions and muons can be used to easily distinguish between the Dirac and Majorana nature of $N$. This method takes advantage of the fact that the flavor of light neutrinos is not identified in the tau decay under consideration. We find that it is particularly advantageous, because of no competing background events, to search for $N$ in the mass range $m_e + m_{\mu} \leqslant m_N \leqslant m_{\mu} + m_{\pi}$, where $m_X$ denotes the mass of particle $X \in \{ e, \mu, \pi, N \}$.
Comment: 6 pages, 5 figures, accepted for publication in Physical Review D