First Lattice QCD Determination of Lepton-Flavor-Universality Ratios in Light-Meson Leptonic Decays

Abstract

The ratio of electronic to muonic leptonic decay widths, $R_{e/\hat{I}¼}$, for the light mesons $\ddot{I}€$ and $K$, provides a clean test of lepton flavor universality (LFU) and a sensitive probe of physics beyond the Standard Model. Its Standard-Model prediction is exceptionally precise, with the leading uncertainty associated with the structure-dependent (SD) radiative correction of $O(0.1\%)$. As experiments such as PIONEER and NA62 aim for unprecedented precision, this SD correction has become an essential ingredient in precision experiment--theory comparisons. We present the first lattice QCD$+$QED calculation of this SD correction at the physical pion mass and in the continuum limit. We employ the infinite-volume reconstruction (IVR) method with Coulomb-gauge photons, significantly reducing both statistical errors and finite-volume effects. We obtain the Standard-Model predictions, $R_{e/\hat{I}¼}=1.23501(10)\times 10^{-4}$ for $\ddot{I}€$ and $R_{e/\hat{I}¼}=2.47653(34)\times 10^{-5}$ for $K$. Our results reduce the hadronic uncertainty in $R_{e/\hat{I}¼}$, provide the most precise Standard-Model predictions to date, and establish first-principles benchmarks for future high-precision tests of LFU.

18 pages, 7 figures