Search for a strangeonium-like structure ${Z}_{s}$ decaying into $\varphi \pi $ and a measurement of the cross section ${e}^{+}{e}^{-}\to \varphi \pi \pi $

Using a data sample of ${e}^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of $108\text{}\text{}{\mathrm{pb}}^{-1}$ collected with the BESIII detector at a center-of-mass energy of 2.125 GeV, we study the process ${e}^{+}{e}^{-}\to \varphi \pi \pi $ and search for a strangeoniumlike structure ${Z}_{s}$ decaying into $\varphi \pi $. No signal is observed in the $\varphi \pi $ mass spectrum. Upper limits on the cross sections for ${Z}_{s}$ production at the 90% confidence level are determined. In addition, the cross sections of ${e}^{+}{e}^{-}\to \varphi {\pi }^{+}{\pi }^{-}$ and ${e}^{+}{e}^{-}\to \varphi {\pi }^{0}{\pi }^{0}$ at 2.125 GeV are measured to be $\left(436.2±6.4±30.1\right)\text{}\text{}\mathrm{pb}$ and $\left(237.0±8.6±15.4\right)\text{}\text{}\mathrm{pb}$, respectively, where the first uncertainties are statistical and the second systematic.