Searches for rare and forbidden kaon decays at the NA62 experiment at CERN

Studies of rare and forbidden $K^{+}$ decays are presented based on analysis of data taken by the NA62 experiment between 2016 and 2018 (Run 1). The primary physics objective of the NA62 experiment is the study of the ultra-rare decay $K^{+}\rightarrow\pi^{+}\nu\bar{\nu}$. Studies of backgrounds are presented and the results of the Run 1 $K^{+}\rightarrow\pi^{+}\nu\bar{\nu}$ analysis are summarised. A search for the $K^{+}\rightarrow\pi^{+}X$ decay, where $X$ is a long-lived feebly interacting particle, is performed through an interpretation of the $K^{+}\rightarrow\pi^{+}\nu\bar{\nu}$ analysis of 2017 data. Upper limits are established on the branching ratio, $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)$ for ranges of $X$ masses, $0$ - $110\,\text{MeV}/c^{2}$ and $154$ - $260\,\text{MeV}/c^{2}$, and lifetimes above $100\,\text{ps}$. Searches for the lepton number violating $K^{+}\rightarrow\pi^{-}\mu^{+}e^{+}$ decay and lepton flavour violating $K^{+}\rightarrow\pi^{+}\mu^{-}e^{+}$ and $\pi^{0}\rightarrow\mu^{+}e^{+}$ decays are described. No signals are observed and upper limits on the branching ratios of these decays at 90% confidence level are obtained: $\mathcal{B}(K^{+}\rightarrow\pi^{-}\mu^{+}e^{+})<4.2\times 10^{-11}$, $\mathcal{B}(K^{+}\rightarrow\pi^{+}\mu^{-}e^{+})<6.6\times10^{-11}$, and $\mathcal{B}(\pi^{0} \rightarrow \mu^{-} e^{+})<3.2\times 10^{-10}$, improving by an order of magnitude on previous results.