Impact of indirect CP violation on Br$(K_S \to \mu^+\mu^-)_{\ell=0}$

TL;DR

This paper examines how indirect CP violation affects the standard-model prediction of the rare decay $K_S o \mu^+\mu^-$ in the zero angular momentum state, revealing a notable shift in the branching ratio.

Contribution

It highlights the enhanced impact of indirect CP violation on the decay's branching ratio and updates the standard-model prediction considering this effect.

Findings

Indirect CP violation causes a few percent shift in the branching ratio.

The impact is amplified by a large amplitude ratio.

Updated standard-model prediction incorporates this effect.

Abstract

The decay $K_S \to (\mu^+\mu^-)_{\ell=0}$, with the final muon pair in an angular-momentum zero state, is a sensitive probe of short-distance physics. It has recently been shown how to extract this branching ratio from neutral kaon decay data. We point out that the impact of indirect CP violation on the standard-model prediction of this mode, while nominally of order $|\epsilon_K| \sim 10^{-3}$, is enhanced by a large amplitude ratio and leads to a shift of the branching ratio Br$(K_S \to \mu^+\mu^-)_{\ell=0}$ by a few percent, depending on the size of a relative phase that can be extracted from data. We also update the standard-model prediction of the short-distance contribution.