The study of two quasi-degenerate heavy sterile neutrinos in rare meson decays

In this work, we study the lepton-number-violating processes of $K^pm$ and $D^pm$ mesons. Two quasi-degenerate sterile neutrinos are assumed to induce such processes. Different with the case where only one sterile neutrino involves, here, the CP phases of the mixing parameters could give sizable contribution. This, in turn, would affect the absolute values of the mixing parameters determined by the experimental upper limits of the branching fractions. A general function which express the difference of the mixing parameters for two-generation and one-generation is presented. Special cases with specific relations of the parameters are discussed. Besides, we also thoroughly investigate the CP violation effect of such processes. It is shown that generally $mathcal A_{CP}$ is a function of the sterile neutrino mass.