Interference Effect in LNV and LNC Meson Decays for 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 $M_1^{+}\to\ell_i^{+}\ell_j^{\pm}\pi^{\mp}$, that arise in a TeV scale Left Right Symmetric model~(LRSM) with nearly degenerate right handed~(RH) neutrinos. LRSM contains three RH neutrinos and a RH gauge boson. The RH neutrinos of masses in the MeV-few GeV range 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 branching ratio of semi-leptonic LNV and LNC meson decays $M_1^{+}\to\ell_i^{+}\ell_j^{+}\pi^{-}$ and $M_1^{+}\to\ell_i^{+}\ell_j^{-}\pi^{+}$ are the same. However, we find, that with at least two RH neutrinos contributing to the process, the LNV and LNC decay rates can differ. Depending on the RH neutrino mixing angles and $CP$ violating phases, the branching ratios for the decay channels $M_1^{+}\to\ell_i^{+}\ell_j^{+}\pi^{-}$ or $M_1^{+}\to\ell_i^{+}\ell_j^{-}\pi^{+}$ can be either enhanced or suppressed.