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Renormalizing a three-flavor lattice calculation of the two-photon contribution to $K_{L} \to μ^{+} μ^{-}$

En-Hung Chao ¹, Norman Christ ², and Ceran Hu ²

¹Center for Theoretical Physics—A Leinweber Institute, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Physics Department, Columbia University, New York City, New York 10027, USA

Phys. Rev. D 114, 074512 – Published 20 October, 2026

DOI: https://doi.org/10.1103/bsqc-6q3t

Abstract

The Standard Model prediction for the rare $K_{L} \to μ^{+} μ^{-}$ decay depends critically on the long-distance contribution coming from the exchange of two photons. Such a contribution can be computed using lattice QCD and an effective three-flavor theory including only the $u$ , $d$ and $s$ quarks, provided terms falling as the inverse square of the omitted charm quark mass, $1 / m_{c}^{2}$ , are neglected. Because of the missing Glashow-Iliopoulos-Maiani cancellation, this three-flavor theory contains additional low-energy constants that depend on $m_{c}$ . Here we show how these constants can be determined from a practical four-flavor lattice QCD calculation performed on a small volume with $u$ and $d$ quark masses that are heavier than physical.

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Phys. Rev. D 114, 074512– Published 20 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 28 July 2026
Accepted 30 September 2026

DOI: https://doi.org/10.1103/bsqc-6q3t

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Renormalizing a three-flavor lattice calculation of the two-photon contribution to $K_{L} \to μ^{+} μ^{-}$

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Renormalizing a three-flavor lattice calculation of the two-photon contribution to KL→μ+μ−

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Renormalizing a three-flavor lattice calculation of the two-photon contribution to $K_{L} \to μ^{+} μ^{-}$