We present a comprehensive calculation of the KL→γ∗γ∗ form factor in dispersion theory, using input from the leptonic decays KL→ℓ+ℓ−γ, KL→ℓ1+ℓ1−ℓ2+ℓ2−, the hadronic mode KL→π+π−γ, the normalization KL→γγ, and the matching to asymptotic constraints. As key result we obtain an improved determination of the long-distance contribution to KL→ℓ+ℓ−, leading to the Standard-Model predictions Br[KL→μ+μ−]=7.44−0.34+0.41×10−9, Br[KL→e+e−]=8.46(37)×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.
@article{arxiv.2310.17689,
title = {Improved Standard-Model prediction for ${K_L\to \ell^+\ell^-}$},
author = {Martin Hoferichter and Bai-Long Hoid and Jacobo Ruiz de Elvira},
journal= {arXiv preprint arXiv:2310.17689},
year = {2024}
}