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Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point

R. Di Palma¹, R. Frezzotti², G. Gagliardi¹, V. Lubicz ¹, G. Martinelli ³, C. T. Sachrajda⁴, F. Sanfilippo ⁵, S. Simula ⁵, and N. Tantalo ²

¹Dipartimento di Matematica e Fisica, Università Roma Tre and INFN, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy
²Dipartimento di Fisica and INFN, Università di Roma “Tor Vergata,” Via della Ricerca Scientifica 1, I-00133 Roma, Italy
³Physics Department and INFN Sezione di Roma La Sapienza, Piazzale Aldo Moro 5, 00185 Roma, Italy
⁴Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom
⁵Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy

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Phys. Rev. D 111, 114523 – Published 30 June, 2025

DOI: https://doi.org/10.1103/r55k-cnqg

Abstract

We present a lattice quantum chromodynamics (QCD) calculation of the radiative leptonic decay rates of the kaon, improving upon our previous work in Desiderio et al. [First lattice calculation of radiative leptonic decay rates of pseudoscalar mesons, Phys. Rev. D 103, 014502 (2021)]. Our analysis uses gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) with $N_{f} = 2 + 1 + 1$ flavors of Wilson-clover twisted mass fermions. For the first time, we go beyond the electroquenched approximation by including quark-disconnected contributions. Several key improvements have been implemented: (i) the simulations are now performed directly at physical light- and strange-quark masses, (ii) finite-size effects are carefully investigated using lattices with spatial extents ranging from $L ≃ 3.8 fm$ to $L ≃ 7.7 fm$ , and (iii) the continuum extrapolation is based on three lattice spacings in the range $a \in [0.08, 0.058] fm$ . As a result of the high-precision determination of the relevant correlation functions, we reduce the uncertainties on both the axial and vector form factors by nearly a factor of two compared to our previous analysis. When compared to experimental measurements in the electron channel ( $K^{-} \to e^{-} {\bar{ν}}_{e} γ$ ), our results show a tension—at the level of 2.6 standard deviations—with respect to KLOE data. On the other hand, they are compatible with measurements from the E36 Collaboration at J-PARC. In the muonic decay channel ( $K^{-} \to μ^{-} {\bar{ν}}_{μ} γ$ ), we confirm the tensions, already observed in our previous study, between lattice QCD predictions and $ISTRA +$ and OKA data, which are both primarily sensitive to the value of the negative-helicity form factor $F^{-}$ .

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Phys. Rev. D 111, 114523– Published 30 June, 2025

Vol. 111, Iss. 11 — 1 June 2025

Received 3 May 2025
Accepted 11 June 2025

DOI: https://doi.org/10.1103/r55k-cnqg

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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Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point

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