Oscillation of heavy sterile neutrino in decay of $B\to \mu e\pi$

In a scenario with two almost mass degenerate heavy sterile Majorana neutrinos with a mass $\sim 1$ GeV, we present the semileptonic decay widths of heavy charged pseudoscalars such as $B$ mesons, either lepton-number-violating ($B^{\pm }\to {\mu }^{\pm }{e}^{\pm }{\pi }^{\mp }$), or lepton-number-conserving ($B^{\pm }\to {\mu }^{\pm }{e}^{\mp }{\pi }^{\pm }$), mediated by such on-shell neutrinos. It had been explained in the literature that such decays may be eventually detected, and that they can present even detectable CP violation effects. In this work we point out that, in addition, such decays may present detectable effects of heavy neutrino oscillation, allowing us to extract the oscillation length and thus the heavy neutrino mass difference $\mathrm{\Delta }{M}_N$, as well as a CP-violating Majorana phase.