A search for the dark photon in the OKA experiment

A search for the massless dark photon in the decay $K^{+}\to \pi^{+}\pi^{0}\overline{{} \gamma}$ is performed with the OKA detector exposed to 17.7 GeV/c RF separated secondary beam of the U70 Proton Synchrotron. A high-statistics data sample of the $K^{+}$ decays is used for a missing mass search of the stable massless invisible dark photon ($\overline{\gamma}$) in the final state. In the absence of a statistically valuable signal the upper limit on the branching ratio of the decay $Br<2.0\times10^{-6}$ is obtained with a 90% confidence level based on a realistic matrix element of the process. Currently, it is the best upper limit for this hypothetical decay channel.