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

Abstract

We present a comparison of existing experimental data for the radiative leptonic decays $P\to \ell \hat{I}{½}_{\ell }{\hat{I}}^3$, where $P=K$ or $\ddot{I}€$ and $\ell =e$ or $\hat{I}¼$, 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, $F_V$ and $F_A$ respectively. These were obtained using lattice QCD+QED simulations at order $O(\hat{I}{\pm }_{\mathrm{em}})$ in the electromagnetic coupling. We find good agreement with the KLOE data on $K\to e\hat{I}{½}_e{\hat{I}}^3$ decays from which the form factor $F^{+}=F_V+F_A$ can be determined. For $K\to \hat{I}¼\hat{I}{½}_{\hat{I}}¼{\hat{I}}^3$ 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 factor $F^{-}=F_V-F_A$ 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.

31 pages, 8 figures, 11 tables. Version to appear in Phys. Rev. D