Lepton universality in a model with three sterile neutrino generations

The $SU(2)_L \times U(1)$ gauge model with an extended lepton sector by three right-handed Majorana sterile neutrinos is considered. Diagonalization of the full $6\times6$ mass matrix of active and sterile neutrinos was carried out. There are two main scenarios that do not contradict cosmological restrictions on sterile dark matter neutrinos: <<exponential mixing>>, in which complex-valued parameters of the mixing matrix can amplify its components by several orders of magnitude, and <<minimal mixing>>, in which there are only masses and mixing parameters of active neutrinos, as well as masses of sterile neutrinos. 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 $pi^+$ and $K^+$ 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 decay width of heavy neutral leptons 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. For the second 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.