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

The structure dependent radiative $K^+ \rightarrow e^+ νγ$ ($K_{e2γ}^{\rm SD^+}$) decay was investigated with stopped positive kaons. The $e^+$ momentum spectra containing 574$\pm$30 $K_{e2γ}^{\rm SD^+}$ events with a $K^+ \rightarrow μ^+ ν$ ($K_{\mu2}$) background of 28$\pm$19 events 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 branching ratio of the $K_{e2γ}^{\rm SD^+}$ decay and the $K^+ \rightarrow e^+ ν$ decay including the internal bremsstrahlung process ($K_{e2(γ)}$). A value of $Br(K_{e2γ}^{\rm SD^+}) / Br(K_{e2(γ)}) = 1.12\pm0.07_{\rm stat} \pm 0.04_{\rm syst}$ was obtained. This indicates a partial branching ratio, $Br(K_{e2γ}^{\rm SD^+}, ~{p_e>200~{\rm MeV}/c}, ~{E_γ>10~{\rm MeV}})/Br(K_{\mu2}) =(1.85 \pm 0.11_{\rm{stat}} \pm 0.07_{\rm{syst}}) \times10^{-5}$, which is $25\%(\sim$2.5$σ)$ higher than the previous experimental result.