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The kaon sector is characterised by several processes which are under activeinvestigation across different experiments. In this work, we present the globalpicture that emerges from a study of the different decay modes. We begin byrevisiting the theoretical component of these decays and providing up-to-datepredictions of the Standard Model as well as the corresponding uncertainties.Several new features emerge, in particular for $K_{S,L}\to \mu\bar\mu$, and arepresented in considerable detail. This offers an ideal platform for extractingthe parameter space supported by the existing data. Motivated by possiblelepton flavour universality violation in $B$ decays, we investigate such Beyondthe Standard Model effects also in rare kaon decays. Without loss ofgenerality, our primary analyses correspond to the paradigm where the Wilsoncoefficients for operators involving tau leptons are chosen to be equal to thatinvolving the muon, i.e. $\delta C^\tau=\delta C^\mu$. We conclude bypresenting the possible picture that can be achieved towards the end of the runof data accumulation in the planned experiments. This includes assumptions onpossible sensitivity goals that the experiments can aim to achieve, in order toextract the kind of physics highlighted in this paper.

Anatomy of kaon decays and prospects for lepton flavour universality violation