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

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

20 pages, 7 figures