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The J-PARC E36 experiment is aiming at searching for the lepton universality violation by precisely measuring the ratio of the branching ratio of the $K^+ \rightarrow e^+ \nu$ ($K_{e2}$) to $K^+ \rightarrow \mu^+ \nu$ ($K_{\mu 2}$) decays. The E36 experiment was performed at J-PARC employing a stopped $K^+$ beam in conjunction with a 12-sector iron-core superconducting toroidal spectrometer. Charged particle momenta were calculated by reconstructing the tracks in the spectrometer. Particle discrimination between $e^+$ and $\mu^+$ was carried out using an aerogel Cherenkov counters and a lead-glass Cherenkov counter, as well as by measuring the time-of-flight between TOF counters.
The peak structure due to the $K_{e2}$ decays was successfully observed in the $e^+$ momentum spectrum. The structure-dependent radiative $K^+ \rightarrow e^+ \nu \gamma$ ($K_{e2 \gamma}^{\rm SD}$) events were selected by requiring one photon hit in the CsI(Tl) calorimeter. The experimental spectra were reproduced by the Monte Carlo simulation, which indicates a correct understanding of the detector acceptance. The $Br(K_{e2 \gamma}^{\rm SD})$ value relative to $Br(K_{e2})$ was obtained by calculating the ratio of the $K_{e2\gamma}$ and $K_{e2}$ yields corrected for their detector acceptances. 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 $Br(K_{e2\gamma}^{\rm SD})/Br(K^+\rightarrow \mu^+ \nu)$.