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

TL;DR

This paper shows that the rare decay $K o\mu^+\mu^-$ can serve as a precise probe of short-distance physics and CKM parameters by measuring the $K_S$ decay rate through interference effects, minimizing long-distance uncertainties.

Contribution

It introduces a method to determine the $K_S o\mu^+\mu^-$ decay rate without separating angular momentum states, enabling clean tests of the Standard Model and CKM matrix elements.

Findings

The decay rate can be experimentally determined via interference effects.

The method reduces hadronic uncertainties below 1%.

It allows extraction of CKM parameters with high precision.

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, ${\cal B}(K_S\to\mu^+\mu^-)_{\ell=0}$ 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 $1\%$.