Search for lepton number and flavour violation in $K^{+}$ and ${\pi }^0$ decays

Searches for the lepton number violating $K^{+} \rightarrow \pi^{-} \mu^{+} e^{+}$decayandtheleptonflavourviolating$K^{+} \rightarrow \pi^{+} \mu^{-} e^{+}$and$\pi^{0} \rightarrow \mu^{-} e^{+}$ decays are reported using data collected by the NA62 experiment at CERN in $2017$-$2018$. No evidence for these decays is found and upper limits of the branching ratios are obtained at 90% confidence level: $\mathcal{B}(K^{+}\to {\pi }^{-}{\mu }^{+}{e}^{+})<4.2\times {10}^{-11}$, $\mathcal{B}(K^{+}\to {\pi }^{+}{\mu }^{-}{e}^{+})<6.6\times {10}^{-11}$ and $\mathcal{B}({\pi }^0\to {\mu }^{-}{e}^{+})<3.2\times {10}^{-10}$. These results improve by one order of magnitude over previous results for these decay modes.