Improved Standard-Model prediction for K L → ℓ + ℓ −

Abstract

Abstract 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.

Keywords

• Kaons
• Rare Decays