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$K \to π γ^{} γ^{}$ transitions at leading order and beyond

Institute of Particle and Nuclear Physics, Charles University, V Holešovičkách 2, 180 00 Prague, Czech Republic and School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom

^*Contact author: tomas.husek@matfyz.cuni.cz; t.husek@bham.ac.uk

Phys. Rev. D 112, 073007 – Published 23 October, 2025

DOI: https://doi.org/10.1103/6dzv-y8jy

Abstract

The transition amplitude of a kaon to a pion and two off-shell photons is studied. First, it is computed at leading order (one-loop level) of the chiral perturbation theory expansion. Explicit analytical results for the leading-order amplitude are presented, constituting the first complete calculation for the doubly off-shell case. Subsequently, it is reevaluated by employing a refined diagrammatic notation and a generic ansatz incorporating effects beyond leading order. The dependence on the underlying $K π P P$ vertex parameters is analyzed. This offers valuable insights into amplitude properties and allows inclusion of unitarity corrections from $K \to 3 π$ , yielding the complete $K \to π γ^{*} γ^{*}$ amplitude structure. Both the charged and neutral channels are treated in parallel. The presented results provide crucial input for phenomenological studies of related rare decays like $K \to π ℓ^{+} ℓ^{-} [γ]$ or $K \to π ℓ_{1}^{+} ℓ_{1}^{-} ℓ_{2}^{+} ℓ_{2}^{-}$ and support ongoing precision measurements at experiments like NA62 at CERN. These results may also find application in other related processes, including $η^{(')}$ decays.

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References (20)

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Phys. Rev. D 112, 073007– Published 23 October, 2025

Vol. 112, Iss. 7 — 1 October 2025

Received 1 July 2025
Accepted 29 August 2025

DOI: https://doi.org/10.1103/6dzv-y8jy

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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$K \to π γ^{} γ^{}$ transitions at leading order and beyond

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K→πγ*γ* transitions at leading order and beyond

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$K \to π γ^{} γ^{}$ transitions at leading order and beyond