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

We study the rare decays of charged π mesons, π+ → e+e+μ−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \overline v $\end{document}μ and π+ → e+μ−e+νe induced by a sterile neutrino N with a mass in the range mμ < mN < mπ . 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.