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

Abstract

We study the rare decays of charged π mesons, π+ to e+ e+ μ- anti-ν_μ and π+ to 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.

20 pages, 8 figures, tex added in the introduction and section 3, equations moved to appendix in section 2

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• CP violation in lepton number violating semihadronic decays of $K,D,D_s,B,B_c$
• Discovering sterile Neutrinos ligther than $M_W$ at the LHC
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• Sensitivity limits on heavy-light mixing $|U_{\mu N}{|}^2$ from lepton number violating $B$ meson decays
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• Left-Right Symmetric Models at the High-Intensity Frontier
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• Exploring CP-violation, via heavy neutrino oscillations, in rare B meson decays at Belle II
• Search for Heavy Sterile Neutrinos in Trileptons at the LHC
• Testing electroweak scale seesaw models at $e^{-}\gamma$ and $\gamma \gamma$ colliders
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• Testing the nature of neutrinos from four-body $\tau$ decays
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• Search for light sterile neutrinos from $W^{\pm }$ decays at the LHC
• Time evolution of cascade decay
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• CP violation in the rare Higgs decays via exchange of on-shell almost degenerate Majorana neutrinos, $H\to {\nu }_k{N}_j\to {\nu }_k{\ell }^{-}U\bar{D}$ and $H\to {\nu }_k{N}_j\to {\nu }_k{\ell }^{+}\bar{U}D$
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