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

We present the comparison of existing experimental data for the radiative leptonic decays P → ℓvℓγ, where P = K or π and ℓ = e or μ, from the KLOE, PIBETA, E787, ISTRA+ and OKA collaborations with the 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 → evγ decays from which the form factor F+ = Fv + FA can be determined. For KK→ μvμγ decays we observe differences of up to 3 - 4 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 factorF− = 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 non-universal corrections to the lepton couplings.