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

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, \({K}_{L}\to {{\ell}}_{1}^{+}{{\ell}}_{1}^{-}{{\ell}}_{2}^{+}{{\ell}}_{2}^{-}\) , 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.