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

We study the rare decays of charged π mesons, π⁺ → e⁺e⁺μ^-ν̄μ and π⁺ → e⁺μ^-e⁺ν_e induced by a sterile neutrino N with a mass in the range m_μ < m_N < m_π. 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.