Measurements of the parameters of the $\phi \mathrm{}\left(1020\right)\mathrm{}$ resonance through studies of the processes $e^{+}{e}^{-}\to K^{+}{K}^{-},$ $K_S{K}_L,$ and ${\pi }^{+}{\pi }^{-}{\pi }^0$

The cross sections of the processes $e^{+}{e}^{-}\to K^{+}{K}^{-},$ $e^{+}{e}^{-}\to K_S{K}_L,$ and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ were measured in the SND experiment at the VEPP-2M collider in the energy region near the $\phi \mathrm{}\left(1020\right)\mathrm{}$ meson. These measurements were based on about ${10}^6$ $K^{+}{K}^{-},$ $0.5\times {10}^6$ $K_S{K}_L,$ and $0.4\times {10}^6$ ${\pi }^{+}{\pi }^{-}{\pi }^0$ selected events. The measured cross sections have been analyzed in the framework of the vector meson dominance model and the main parameters of the $\phi$ resonance were obtained, such as its mass, width, the production cross section, and branching ratios of the main decay modes. The measured value of the $\phi$ meson total width, ${\Gamma }_{\phi }=4.21\mathrm{}\pm 0.04,$ is lower than the present world average of $4.458\pm 0.032$ MeV. Contributions in addition to the conventional vector meson dominance model were found in the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ reaction cross section.