Rare K decays off and on the lattice

Abstract

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 ${\epsilon }^{\prime }$. 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.

Comments: 8 pages, to appear in the proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermilab