Lattice calculation of light meson radiative leptonic decays

Abstract

In this work, we perform a lattice QCD calculation of the branching ratios and the form factors of radiative leptonic decays P → ℓν_ℓγ (P = π, K) using N_f = 2 + 1 domain wall fermion ensembles generated by the RBC and UKQCD collaborations at the physical pion mass. We adopt the infinite-volume reconstruction (IVR) method, which extends lattice data to infinite volume and effectively controls the finite-volume effects. This study represents a first step toward a complete calculation of radiative corrections to leptonic decays using the IVR method, including both real photon emissions and virtual photon loops. For decays involving a final-state electron, collinear radiative corrections, enhanced by the large logarithmic factors such as ln(m²_π/m²_e) and ln(m²_K/m²_e),can reach the level of O(10%) and are essential at the current level of theoretical and experimental precision. After including these corrections, our result for π → eν_eγ agrees with the PIBETA measurement; for K → eνeγ, our results are consistent with the KLOE data and exhibit a 1.7σtension with E36; and for K → µν_µγ, where radiative corrections are negligible, our results confirm the previously observed discrepancies between lattice results and the ISTRA/OKA measurements at large photon energies, and with the E787 results at large muon–photon angles.

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