Study of the decay $$K^{+}\rightarrow \pi ^{+}\pi ^{-}\pi ^{+}\gamma $$ K+→π+π-π+γ in the OKA experiment

Abstract A high statistics data sample of the decays of $$K^+$$ 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 $$K^{+}\rightarrow \pi ^{+}\pi ^{-}\pi ^{+}\gamma $$ K+→π+π-π+γ decays with the energy of the photon in the kaon rest frame greater than 30 MeV. The measured branching fraction of the $$K^{+}\rightarrow \pi ^{+}\pi ^{-}\pi ^{+}\gamma $$ K+→π+π-π+γ , with $$E_{\gamma }^{*} > 30\ \hbox {MeV}$$ Eγ∗>30MeV is equal to $$(0.71 \pm 0.05) \times 10^{-5}$$ (0.71±0.05)×10-5 . The measured differential branching fraction over photon energy is compared with the prediction of the chiral perturbation theory to $${\mathcal {O}}(p^{4})$$ O(p4) . A search for an up-down asymmetry of the photon with respect to the hadronic system decay plane is also performed.