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Exploratory calculation of $K_{L} \to μ^{+} μ^{-}$ decay from lattice QCD at physical pion mass

Peter Boyle ^1,2, En-Hung Chao ³, Norman Christ ³, Ceran Hu ³, Luchang Jin ⁴, and Yidi Zhao ³

¹Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
²School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
³Physics Department, Columbia University, New York City, New York 10027, USA
⁴Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, USA

Phys. Rev. D 113, 074523 – Published 30 April, 2026

DOI: https://doi.org/10.1103/22hn-ymsd

Abstract

We compute the complex, long-distance two-photon-exchange amplitude which contributes to the rare $K_{L} \to μ^{+} μ^{-}$ decay from lattice QCD. We use a $24^{3} \times 64$ physical-pion-mass gauge field ensemble at an inverse lattice spacing of 1.023 GeV and a ${QED}_{\infty}$ -based formalism. Our implementation strategies for all five non-SU(3)-flavor-suppressed diagram topologies are given in detail. We achieve a 25% statistical precision on the dispersive part of this long-distance amplitude. This calculation is carried out with $2 + 1$ quark flavors and therefore requires the addition of counterterms to compensate for the absence of the Glashow-Iliopoulos-Maiani mechanism. These counterterms are not included in the current calculation and will be the subject of a second paper. Although a direct comparison to experiment cannot yet be made because of those omitted counterterms, the present exploratory calculation allows one to identify principal sources of statistical uncertainty in this calculation. The precision of our results is limited by the reconstruction of the physical contribution of the $η$ intermediate state, for which various strategies are tested and compared.

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Phys. Rev. D 113, 074523– Published 30 April, 2026

Vol. 113, Iss. 7 — 1 April 2026

Received 23 September 2025
Accepted 2 April 2026

DOI: https://doi.org/10.1103/22hn-ymsd

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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Exploratory calculation of $K_{L} \to μ^{+} μ^{-}$ decay from lattice QCD at physical pion mass

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Exploratory calculation of KL→μ+μ− decay from lattice QCD at physical pion mass

Abstract

Physics Subject Headings (PhySH)

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References (56)

Exploratory calculation of $K_{L} \to μ^{+} μ^{-}$ decay from lattice QCD at physical pion mass