Standard Model and New Physics contributions to $K_L$ and $K_S$ into four leptons

Abstract

We study the $K_L$ and $K_S$ decays into four leptons ($e\bar{e}e\bar{e},\mu \bar{\mu }\mu \bar{\mu },e\bar{e}\mu \bar{\mu }$) where we use a form factor motivated by vector meson dominance, and show the dependence of the branching ratios and spectra from the slopes. A precise determination of short distance contribution to $K_L\to \mu \mu$ is affected by our ignorance on the sign of the amplitude $\mathcal{A}(K_L\to \gamma \gamma )$ but we show a possibility to measure the sign of this amplitude by studying $K_L$ and $K_S$ decays in four leptons. We also investigate the effect of New Physics contributions for these decays.

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