Study of the decay $K^{+}topi^{+}pi^{-}pi^{+}gamma$ in the OKA experiment

A high statistics data sample of the decays of $K^+$ mesons to three charged particles was accumulated by the OKA experiment in 2012 and 2013. This allowed to select a clean sample of about 450 events with $K^{+}topi^{+}pi^{-}pi^{+}gamma$ decays with the energy of the photon in the kaon rest frame greater than 30 MeV. The measured branching fraction of the $K^{+}topi^{+}pi^{-}pi^{+}gamma$, with $E_{gamma}^{*}$ > 30 MeV is $(0.71 pm 0.05) times 10^{-5}$. The measured energy spectrum of the decay photon is compared with the prediction of the chiral perturbation theory to O$(p^{4})$. A search for an up-down asymmetry of the photon with respect to the hadronic system decay plane is also performed.