Rare K decays off and on the lattice

TL;DR

This paper discusses the significance of rare K decays, especially $K_L o \pi^0 u ar u$, in understanding the kaon unitarity triangle, emphasizing theoretical calculations and experimental challenges, with a focus on lattice studies and future experiments.

Contribution

It highlights the importance of improving theoretical predictions and experimental measurements of rare K decays, particularly $K^0 o \pi^0 \mu^+ \mu^-$, for advancing kaon physics.

Findings

The decay $K_L o \\pi^0 \\nu \\bar \\nu$ is theoretically clean but experimentally challenging.

Current Standard Model predictions are two orders of magnitude below experimental bounds.

Lattice and experimental efforts are crucial for progress in rare K decay studies.

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 $\varepsilon'$. 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.