Direct CP Violation in $K \rightarrow \mu ^+ \mu ^-$

Abstract

The upgrade of the LHCb experiment will probe a rare decay $K_S \rightarrow \mu ^+ \mu ^-$ precisely. Although the process is dominated by CP-conserving decay, one can extract CP-violating pieces via the precise measurement. In this contribution, I introduce an interference contribution between $K_L$ and $K_S$ that is sensitive to a direct CP violation. It is found that the interference contribution can affect $\text {Br}(K_S\rightarrow \mu ^+ \mu ^-$) Standard Model prediction up to $60\,\%$. It is also found that an unknown sign of an amplitude of $K_L \rightarrow \gamma \gamma$ can be determined by measuring the interference effect, which can much reduce a theoretical uncertainty of $\text {Br}(K_L \rightarrow \mu ^+ \mu ^-$). I also show that the interference contributions in new physics models and their correlations with other kaon rare decays, especially $\varepsilon ^{\prime }/\varepsilon$. This contribution is based on D’Ambrosio and Kitahara in Phys Rev Lett 119:201802, 2017, Chobanova et al. in JHEP 1805:024, 2018, Endo et al. in JHEP 1804:019, 2018.