Measurement of structure dependent radiative $K^{+} \rightarrow e^{+} \nu \gamma$ decays using stopped positive kaons.

The structure dependent radiative $K^+ \rightarrow e^+ \nu \gamma$ ($K_{e2\gamma}^{\rm SD}$) decay was investigated with stopped positive kaons. The $e^+$ momentum spectra were measured with and without a photon in coincidence and analyzed with Monte Carlo simulations for acceptance and detector response to extract the ratio of the $K_{e2\gamma}^{\rm SD}$ and $K^+ \rightarrow e^+ \nu$ ($K_{e2}$) branching ratios. A value of $Br(K_{e2\gamma}^{\rm SD}) / Br(K_{e2}) = 1.22\pm0.07_{\rm stat} \pm 0.04_{\rm syst}$ was obtained, which is significantly larger than the value inferred from a previous experimental result for $Br(K_{e2\gamma}^{\rm SD})/Br(K^+\rightarrow \mu^+ \nu)$.