Searching for heavy sterile neutrinos in kaon decays

We present here a study of the impact of a heavy neutrino (or heavy neutral lepton) on leptonic and semileptonic kaon decays. We used a simplified model consisting of 3 light neutrinos responsible for neutrino oscillations and a heavy sterile neutrino. We found that it can lead to large deviations from the Standard Model predictions for leptonic decays, in conflict with experimental measurements of $K_{e2}$ and the lepton universality test $R_K$. This allows to derive new constraints on the leptonic mixing for heavy sterile neutrinos. No tension was found when considering the semileptonic decays. Finally, we point out the potential of the decay $K_L\to \nu \nu$ as a clear signature of physics beyond the Standard Model.