Study of the decay $K^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}\gamma$ 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 $K^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}\gamma$ decays with the energy of the photon in the kaon rest frame greater than 30 MeV. The measured branching fraction of the $K^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}\gamma$, with $E_{\gamma }^{\ast }$ > 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.