Sterile neutrinos in lepton number and lepton flavor violating decays

We study the contribution of massive dominantly sterile neutrinos, $N$, to the Lepton Number and Lepton Flavor Violating semileptonic decays of $\tau$ and $B, D, K$-mesons. We focus on special domains of sterile neutrino masses $m_{N}$ where it is close to its mass-shell. This leads to an enormous resonant enhancement of the decay rates of these processes. This allows us to derive stringent limits on the sterile neutrino mass $m_{N}$ and its mixing $U_{\alpha N}$ with active flavors. We apply a joint analysis of the existing experimental bounds on the decay rates of the studied processes. In contrast to other approaches in the literature our limits are free from ad hoc assumptions on the relative size of the sterile neutrino mixing parameters. We analyze the impact of this sort of assumptions on the extraction of the limits on $m_{N}$ and $U_{\alpha N}$, and discuss the effect of finite detector size. Special attention was paid to the limits on meson decays with $e^{\pm}e^{\pm}$ in final state, derived from non-observation of $0\nu\beta\beta$-decay. We point out that observation of these decays may, in particular, shed light on the Majorana phases of the neutrino mixing matrix.