Measurements of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>η</mml:mi></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>K</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:msup><mml:mi>K</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>∓</mml:mo></mml:msup></mml:math>cross sections using initial state radiation events

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