Signature of the triangle singularity in the reaction $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$

The singularity caused by the decay kinematics in the vertices of the triangle diagram is shown to imply the distortion of the patterns of $\rho \omega$ interference in the ${\pi }^{+}{\pi }^{-}$ mass spectrum of the reaction $e^{+}{e}^{-}\to \rho \pi +\omega \pi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ at energies in the range $0.95 \mathrm{GeV}\le \sqrt{s}\le 1.4 \mathrm{GeV}$. In the total cross section the singularity manifests itself as a measurable decrease of the cross section magnitude at energies in between $\omega$ and $\varphi$ peaks. The studies of the effect at $e^{+}{e}^{-}$ colliders with a luminosity of $L={10}^{31}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\mathrm{s}}^{-1\mathrm{}}$ or higher could be of great interest as a tool for testing the self-consistency of calculations going beyond the tree approximation and as a possibility to obtain additional information on the mechanisms of the OZI rule and $G$ parity breakings.