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

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, ${\cal B}(K_S\to\mu^+\mu^-)_{\ell=0}$ can be experimentally determined without the need to separate the $\mathrm{\ell }=0$ and $\mathrm{\ell }=1$ 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 $\mid V_{ts}{V}_{td}\sin (\beta +{\beta }_s)\mid \approx \mathrm{\mid }{A}^2{\lambda }^5\bar{\eta }\mathrm{\mid }$ with hadronic uncertainties below $1\mathrm{\%}$.