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, \({K}_{L}\to {{\ell}}_{1}^{+}{{\ell}}_{1}^{-}{{\ell}}_{2}^{+}{{\ell}}_{2}^{-}\), 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.
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Acknowledgments
We thank Michael Akashi-Ronquest and John Belz for correspondence on refs. [84, 85], and Gino Isidori for discussions on ref. [12]. We further thank Joachim Brod, Giancarlo D’Ambrosio, Martin Gorbahn, and Marc Knecht for discussions during the meeting Kaons@CERN 2023. Financial support by the SNSF (Project No. PCEFP2_181117) and by the Ramón y Cajal program (RYC2019-027605-I) of the Spanish MINECO is gratefully acknowledged.
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Hoferichter, M., Hoid, BL. & de Elvira, J.R. Improved Standard-Model prediction for KL → ℓ+ℓ−. J. High Energ. Phys. 2024, 71 (2024). https://doi.org/10.1007/JHEP04(2024)071
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DOI: https://doi.org/10.1007/JHEP04(2024)071