Interference effect in lepton number violating and conserving meson decays for a left-right symmetric model

We study the effect of interference on the lepton number violating~(LNV) and lepton number conserving~(LNC) three-body meson decays $M_1^{+}\to l_i^{+} l_j^{\pm}\pi^{\mp}$, that arise in a TeV scale Left Right Symmetric model~(LRSM) with degenerate or nearly degenerate right handed~(RH) neutrinos. LRSM contains three RH neutrinos and a RH gauge boson. The RH neutrinos with masses in the range of $M_N \sim$ (MeV - few GeV) can give resonant enhancement in the semi-leptonic LNV and LNC meson decays. In the case, where only one RH neutrino contributes to these decays, the predicted new physics branching ratio of semi-leptonic LNV and LNC meson decays $M_1^{+}\to l_i^{+} l_j^{+}\pi^{-}$ and $M_…