Structure at 2175 MeV in<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:mi>ϕ</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>observed via initial-state radiation

We study the initial-state-radiation processes ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$ using an integrated luminosity of $232\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected at the $\ensuremath{\Upsilon}(4S)$ mass with the BABAR detector at SLAC. Even though these reactions are dominated by intermediate states with excited kaons, we are able to study for the first time the cross section for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\phi}(1020){f}_{0}(980)$ as a function of center-of-mass energy. We observe a structure near threshold consistent with a ${1}^{--}$ resonance with mass $m=2.175\ifmmode\pm\else\textpm\fi{}0.010\ifmmode\pm\else\textpm\fi{}0.015\text{ }\text{ }\mathrm{GeV}/{c}^{2}$ and width $\ensuremath{\Gamma}=58\ifmmode\pm\else\textpm\fi{}16\ifmmode\pm\else\textpm\fi{}20\text{ }\text{ }\mathrm{MeV}$. We observe no $Y(4260)$ signal and set a limit of ${\mathcal{B}}_{Y\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}}\ifmmode\cdot\else\textperiodcentered\fi{}{\ensuremath{\Gamma}}_{ee}^{Y}&lt;0.4\text{ }\text{ }\mathrm{eV}$ (90% confidence level), which excludes some models.