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

TL;DR

This paper improves the Standard-Model predictions for the rare decays of the neutral kaon into lepton pairs by calculating the relevant form factors using dispersion theory and multiple experimental inputs, reducing uncertainties.

Contribution

It provides a comprehensive dispersion-theoretic calculation of the $K_L\to\gamma^*\gamma^*$ form factor, leading to more precise Standard-Model predictions for $K_L\to\ell^+\ell^-$ decays.

Findings

Predicted branching ratio for $K_L\to\mu^+\mu^-$: $7.44^{+0.41}_{-0.34} \times 10^{-9}$

Predicted branching ratio for $K_L\to e^+e^-$: $8.46(37) \times 10^{-12}$

More stringent limits on physics beyond the Standard Model

Abstract

We present a comprehensive calculation of the $K_L\to\gamma^*\gamma^*$ 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 $\text{Br}[K_L\to\mu^+\mu^-]=7.44^{+0.41}_{-0.34}\times 10^{-9}$, $\text{Br}[K_L\to e^+e^-]=8.46(37)\times 10^{-12}$, 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.