Improved Standard-Model prediction for KL → ℓ+ℓ−

A bstract We present a comprehensive calculation of the K L → γ ∗ γ ∗ form factor in dispersion theory, using input from the leptonic decays K L → ℓ + ℓ − γ , KL→ ₁⁺₁⁻₂⁺₂⁻ , the hadronic mode K L → π + π − γ , the normalization K L → γγ , and the matching to asymptotic constraints. As key result we obtain an improved determination of the long-distance contribution to K L → ℓ + ℓ − , leading to the Standard-Model predictions Br[ K L → μ + μ − ] = 7.44-0.34+0.41 × 10 − 9 , Br[ K L → 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.