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

We study the effect of interference on lepton number violating~(LNV) and 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 right handed~(RH) neutrinos. LRSM contains three RH neutrinos gauge boson. The masses range $M_N \sim$ (MeV - few GeV) can give resonant enhancement semi-leptonic LNV LNC decays. In case, where only one neutrino contributes to these decays, predicted new physics branching ratio l_j^{+}\pi^{-}$ l_j^{-}\pi^{+}$ are equal. find at least two contributing process, decay rates differ. Depending mixing angles $CP$ violating phases, ratios channels mediated by heavy be either enhanced suppressed, differ from unity.