Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$

Abstract

We present a comprehensive calculation of the $K_L\to {\gamma }^{\ast }{\gamma }^{\ast }$ form factor in dispersion theory, using input from the leptonic decays $K_L\to {\ell }^{+}{\ell }^{-}\gamma$, $K_L\to {\ell }_1^{+}{\ell }_1^{-}{\ell }_2^{+}{\ell }_2^{-}$, the hadronic mode $K_L\to {\pi }^{+}{\pi }^{-}\gamma$, the normalization $K_L\to \gamma \gamma$, and the matching to asymptotic constraints. As key result we obtain an improved determination of the long-distance contribution to $K_L\to {\ell }^{+}{\ell }^{-}$, leading to the Standard-Model predictions $\text{Br}[K_L\to {\mu }^{+}{\mu }^{-}]=7.44_{-0.34}^{+0.41}\times 10^{-9}$, $\text{Br}[K_L\to e^{+}{e}^{-}]=8.46(37)\times 10^{-12}$, and more stringent limits on physics beyond the Standard Model. We provide a detailed breakdown of the current uncertainty, and delineate how future experiments and the interplay with lattice QCD could help further improve the precision.

39 pages, 6 figures; version published in JHEP

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• CP violation in $K\to {\mu }^{+}{\mu }^{-}$ with and without time dependence through a tagged analysis