Searches for lepton number violating $K^{+}\to {\pi }^{-}({\pi }^0)e^{+}{e}^{+}$ decays

Searches for lepton number violating $K^{+}\to {\pi }^{-}{e}^{+}{e}^{+}$ and $K^{+}\to {\pi }^{-}{\pi }^0{e}^{+}{e}^{+}$ decays have been performed using the complete dataset collected by the NA62 experiment at CERN in 2016-2018. Upper limits of $5.3\times {10}^{-11}$ and $8.5\times {10}^{-10}$ are obtained on the decay branching fractions at 90% confidence level. The former result improves by a factor of four over the previous best limit, while the latter result represents the first limit on the $K^{+}\to {\pi }^{-}{\pi }^0{e}^{+}{e}^{+}$ decay rate.