Searches for lepton flavor and lepton number violation in $K^+$ decays with NA62

The NA62 experiment at the CERN SPS provides unique opportunity to study rare and forbidden decays of $K^{+}$ mesons. Using the data collected in 2017 a search for the lepton number violating decays $K^{+}$ → $\pi^-$ $\mu^+$ $\mu^+$and $K^{+}$ → $\pi^-$ $e^{+}$ $e^{+}$ has been performed. New upper limits on the branching ratio have been obtained: 4.2×10$^{-11}$ for the muon and 2.2×10$^{-10}$ for the electron mode (90% confidence level). These results improve the existing limits by factors of 2 and 3 respectively.