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

Abstract

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, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${K}_{L}\ o {{\\ell}}_{1}^{+}{{\\ell}}_{1}^{-}{{\\ell}}_{2}^{+}{{\\ell}}_{2}^{-}$$\\end{document}, 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−] = \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${7.44}_{-0.34}^{+0.41}$$\\end{document} × 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.