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.
Highlights
The decays of charged pseudoscalar mesons into light leptons, P → lνl1⁄2γ where l stands for an electron or a muon, represent an important contribution to flavor physics since they give access to fundamental parameters of the Standard Model (SM), in particular to the CabibboKobayashi-Maskawa (CKM) matrix elements [1]
We present a comparison of existing experimental data for the radiative leptonic decays P → lνlγ, where P 1⁄4 K or π and l 1⁄4 e or μ, from the KLOE, PIBETA, E787, ISTRAþ 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
We find good agreement with the KLOE data on K → eνeγ decays from which the form factor Fþ 1⁄4 FV þ FA can be determined
Summary
The decays of charged pseudoscalar mesons into light leptons, P → lνl1⁄2γ where l stands for an electron or a muon, represent an important contribution to flavor physics since they give access to fundamental parameters of the Standard Model (SM), in particular to the CabibboKobayashi-Maskawa (CKM) matrix elements [1]. In addition to the leptonic decay constant fP, there are other structure-dependent (SD) amplitudes describing the emission of real photons from hadronic states, usually parametrized in terms of the vector and axialvector form factors, FV and FA respectively. [8], where the pt and SD amplitudes for real photon emission have been determined nonperturbatively in numerical lattice QCD þ QED simulations at order OðαemÞ in the electromagnetic coupling.
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