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

TL;DR

This paper compares lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data, revealing good agreement in some cases and notable discrepancies in others, highlighting the need for improved measurements and models.

Contribution

It provides the first non-perturbative lattice QCD+QED calculations of structure-dependent form factors for light meson decays and compares them with experimental results, identifying areas of tension.

Findings

Good agreement for $K o e u_e\gamma$ decays.

Discrepancies of 3-4 standard deviations at large photon energies for $K o \mu u_\mu\gamma$ decays.

Poor overall fit when combining all kaon decay data within the Standard Model.

Abstract

We present a comparison of existing experimental data for the radiative leptonic decays $P\to\ell\nu_\ell\gamma$, where $P=K$ or $\pi$ and $\ell=e$ or $\mu$, 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 $O(\alpha_{\mathrm{em}})$ in the electromagnetic coupling. We find good agreement with the KLOE data on $K\to e\nu_e\gamma$ decays from which the form factor $F^+=F_V+F_A$ can be determined. For $K\to\mu\nu_\mu\gamma$ 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.