Measurement of the $T$-odd correlation in the $K^+ \rightarrow \pi^{0} e^{+} \nu_{e} \gamma$ radiative decay at the OKA setup

The $T$-odd correlation $\xi_{\pi e\gamma }$, which is the mixed product of the momenta of $e^+$, $\pi^0$, and $\gamma$ in the system of rest of the kaon divided by $M_K^3$, has been measured in the $K^+ \rightarrow \pi^{0} e^{+} \nu_{e} \gamma $ radiative decay among $101\,200$ candidate events detected at the OKA setup. The asymmetry of the distribution in $\xi_{\pi e\gamma }$ is characterized by the ratio $A_{\xi}= \frac {N_{+}-N_{-}} {N_{+}+N_{-}}$, where $N_{+(-)}$ is the number of events with positive (negative) $\xi$. The value $A_{\xi} = (+0.1 \pm 3.9\,($stat.$) \pm1.7\,($syst.$))\times10^{-3}$ or $|A_{\xi}| < 5.4\times10^{-3}$ ($90\%$ C.L.) has been obtained.