Lepton universality in a model with three generations of sterile Majorana neutrinos

The extension of the Standard Model lepton sector by three right-handed Majorana neutrinos (heavy neutral leptons, HNL) with masses up to GeV scale is considered. While the lightest HNL is the dark matter particle with mass of the order of 5 keV, the remaining two HNLs ensure standard (active) neutrino mass generation by means of the see-saw type I mechanism. Two heavy sterile neutrinos with quasi-degenerate masses up to 5 GeV can induce the deviation of lepton universality violation parameter in the decays of $\pi^\pm$ and $K^\pm$ mesons from the the Standard Model value. Contours are obtained for the permissible values of this parameter within the framework of two mixing scenarios, taking into account the lifetime boundary for heavy neutral lepton from Big Bang nucleosynthesis in the Universe. When calculating the HNL decay width in the framework of the model with six Majorana neutrinos, three active and three heavy, both two-particle and three-particle lepton decays, essential for masses below the mass of the pion, were taken into account. When calculating the decay widths, the limiting case known as the "Dirac limit" is not used. The results based on the explicit form of mixing matrices for three HNL generations and the diagram technique for Majorana neutrinos, which explicitly take into account the interference terms for diagrams with identical mass states, can lead to some differences in lifetime from the results using the "Dirac limit" and the displacement of the corresponding experimental exclusion contours of the "mass-mixing" type. For the second mixing scenario, a mass region of $460~\text{MeV} <M< 485$ MeV has been found that allows violation of lepton universality in charged kaon decays at the level observed in the experiment.