Measurements of $e^{+}{e}^{-}\to K^{+}{K}^{-}\eta$, $K^{+}{K}^{-}{\pi }^0$, and $K_s^0{K}^{\pm }{\pi }^{\mp }$ cross sections using initial state radiation events

This paper reports measurements of processes: $e^{+}{e}^{-}\to \gamma K_S^0{K}^{\pm }{\pi }^{\mp }$, $e^{+}{e}^{-}\to \gamma K^{+}{K}^{-}{\pi }^0$, $e^{+}{e}^{-}\to \gamma \varphi \eta$, and $e^{+}{e}^{-}\to \gamma \varphi {\pi }^0$. The initial-state radiated photon allows to cover the hadronic final state in the energy range from thresholds up to $\approx 4.6\mathrm{GeV}$. The overall size of the data sample analyzed is $232{\mathrm{fb}}^{-1}$, collected by the BABAR detector running at the PEP-II $e^{+}{e}^{-}$ storage ring. From the Dalitz plot analysis of the $K_S^0{K}^{\pm }{\pi }^{\mp }$ final state, moduli, and relative phase of the isoscalar and the isovector components of the $e^{+}{e}^{-}\to K{K}^{*}(892)$ cross section are determined. Parameters of $\varphi$ and $\rho$ recurrences are also measured, using a global fitting procedure which exploits the interconnection among amplitudes, moduli, and phases of the $e^{+}{e}^{-}\to K_S^0{K}^{\pm }{\pi }^{\mp }$, $K^{+}{K}^{-}{\pi }^0$, $\varphi \eta$ final states. The cross section for the OZI-forbidden process $e^{+}{e}^{-}\to \varphi {\pi }^0$, and the $J/\psi$ branching fractions to $K{K}^{*}(892)$ and $K^{+}{K}^{-}\eta$ are also measured.