Probing Majorana neutrinos in rare π+ → e+e+μ-ν decays

We study the rare decays of charged pi mesons, pi(+) -> e(+)e(+)mu(-)(nu) over bar (mu) and pi(+) -> e(+)mu(-)e(+)nu(e) induced by a sterile neutrino N with a mass in the range m(mu) < m(N) < m(pi). The first process violates Lepton Number by two units and so occurs only if N is Majorana, while the second process conserves Lepton Number and occurs irrespective of the Majorana or Dirac character of N. We study a way to distinguish the Majorana vs. Dirac character of N in these processes using the mum spectrum. We also find that the branching ratios could be at the reach of high luminosity experiments like Project X at FNAL or any proposed neutrino (or muon) factories worldwide.