Study of $K^{+}\to \ddot{I}{€}^0{e}^{+}\hat{I}½{\hat{I}}^3$ decay with OKA setup

Abstract

Results of a study of the $K^{+}\to \ddot{I}{€}^0{e}^{+}\hat{I}½{\hat{I}}^3$ decay at OKA setup are presented. More than 32000 events of this decay are observed. The differential spectra over the photon energy and the photon-electron opening angle in kaon rest frame are presented. The branching ratios, normalized to that of $K_{e3}$ decay are calculated for different cuts in $E_{\hat{I}}^3$ and $cos\hat{I}{˜}_{e{\hat{I}}^3}^{\ast }$. In particular, the branching ratio for $E_{\hat{I}}^3>30$ MeV and $\hat{I}{˜}_{e{\hat{I}}^3}^{\ast }>20^{\circ }$ is measured R = $\frac{Br(K^{+}\to \ddot{I}{€}^0{e}^{+}\hat{I}{½}_e{\hat{I}}^3)}{Br(K^{+}\to \ddot{I}{€}^0{e}^{+}\hat{I}{½}_e)}$ = =(0.587$\pm$0.010($stat.$)$\pm$0.015($syst.$))$\times 10^{-2}$, which is in a good agreement with ChPT $O(p^4)$ calculations.