$K\to {\mu }^{+}{\mu }^{-}$ as a clean probe of short-distance physics

Abstract

The $K\to {\mu }^{+}{\mu }^{-}$ decay is often considered to be uninformative of fundamental theory parameters since the decay is polluted by long-distance hadronic effects. We demonstrate that, using very mild assumptions and utilizing time-dependent interference effects, $\mathcal{B}(K_S\to {\mu }^{+}{\mu }^{-}{)}_{\ell =0}$ can be experimentally determined without the need to separate the $\ell =0$ and $\ell =1$ final states. This quantity is very clean theoretically and can be used to test the Standard Model. In particular, it can be used to extract the CKM matrix element combination $\left|V_{ts}{V}_{td}\sin (\beta +{\beta }_s)\right|\approx |A^2{\lambda }^5\bar{\eta }|$ with hadronic uncertainties below $1\%$.