Probing Majorana neutrinos in rare pi+ to e+ e+ mu- nu decays

We study the rare decays of charged \pi\ mesons, \pi+ to e+ e+ \mu- anti-\nu_\mu\ and \pi+ to 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 muon 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.