Comparison of lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data

We present a comparison of existing experimental data for the radiative leptonic decays P→ℓνℓγ, where P=K or π and ℓ=e or μ, from the KLOE, PIBETA, E787, ISTRA+ and OKA collaborations with theoretical predictions based on the recent non-perturbative determinations of the structure-dependent vector and axial-vector form factors, FV and FA respectively. These were obtained using lattice QCD+QED simulations at order O(αem) in the electromagnetic coupling. We find good agreement with the KLOE data on K→eνeγ decays from which the form factor F+=FV+FA can be determined. For K→μνμγ decays we observe differences of up to -34 standard deviations at large photon energies between the theoretical predictions and the data from the E787, ISTRA+ and OKA experiments and similar discrepancies in some kinematical regions with the PIBETA experiment on radiative pion decays. A global study of all the kaon-decay data within the Standard Model results in a poor fit, largely because at large photon energies the KLOE and E787 data cannot be reproduced simultaneously in terms of the same form factor F+. The discrepancy between the theoretical and experimental values of the form factor F-=FV-FA is even more pronounced. These observations motivate future improvements of both the theoretical and experimental determinations of the structure-dependent form factors F+ and F-, as well as further theoretical investigations of models of "new physics"which might for example, include possible flavor changing interactions beyond V-A and/or nonuniversal corrections to the lepton couplings.