Comparison of lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>QCD</mml:mi><mml:mo>+</mml:mo><mml:mi>QED</mml:mi></mml:mrow></mml:math> 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 $P\ensuremath{\rightarrow}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}\ensuremath{\gamma}$, where $P=K$ or $\ensuremath{\pi}$ and $\ensuremath{\ell}=e$ or $\ensuremath{\mu}$, from the KLOE, PIBETA, E787, $\mathrm{ISTRA}+$ 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 $\mathrm{QCD}+\mathrm{QED}$ simulations at order $O({\ensuremath{\alpha}}_{\mathrm{em}})$ in the electromagnetic coupling. We find good agreement with the KLOE data on $K\ensuremath{\rightarrow}e{\ensuremath{\nu}}_{e}\ensuremath{\gamma}$ decays from which the form factor ${F}^{+}={F}_{V}+{F}_{A}$ can be determined. For $K\ensuremath{\rightarrow}\ensuremath{\mu}{\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\gamma}$ decays we observe differences of up to --34 standard deviations at large photon energies between the theoretical predictions and the data from the E787, $\mathrm{ISTRA}+$ 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 ${F}^{\ensuremath{-}}={F}_{V}\ensuremath{-}{F}_{A}$ is even more pronounced. These observations motivate future improvements of both the theoretical and experimental determinations of the structure-dependent form factors ${F}^{+}$ and ${F}^{\ensuremath{-}}$, as well as further theoretical investigations of models of ``new physics'' which might for example, include possible flavor changing interactions beyond $V\ensuremath{-}A$ and/or nonuniversal corrections to the lepton couplings.

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