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$K\to πν\barν$ in the Standard Model and Beyond

The precision expected for the rare $K\to πν\barν$ decays by the NA62 and KOTO experiments in the coming decade will rival their current SM predictions. In preparation for this upcoming opportunity, we review the SM predictions and discuss the sensitivity of these decays to models beyond the Standard Model, considering in particular simplified Z and Z' models as benchmarks. In the latter case we also discuss how these decays could ultimately probe distance scales as small as zeptometers i.e. peek into the Zeptouniverse.