Rare K decays off and on the lattice

The importance of rare $K$ decays especially in the context of a kaon unitarity triangle (KUT) is emphasized. The decay $K_L\to {\pi }^0\nu \bar{\nu }$ is theoretically very clean but experimentally extremely challenging. The Standard Model prediction $\mathcal{B}\sim 3\times {10}^{-11}$ is still about two orders of magnitude away from the current experimental upper bound. One way to continue to make progress towards the construction of a KUT is by improving the accuracy in the calculation of ${\epsilon }^{\mathrm{\prime }}$. Another way which is the primary focus here is via studies of $K^0\to {\pi }^0{\mu }^{+}{\mu }^{-}$. LHCb, J-PARC, the proposed HIKE project, phenomenology, and in fact precision studies on the lattice can all play a very important role in this context.