Two charged strangeonium-like structures observable in the $Y(2175)\to \varphi (1020){\pi }^{+}{\pi }^{-}$ process

Via the Initial Single Pion Emission (ISPE) mechanism, we study the $\varphi (1020){\pi }^{+}$ invariant mass spectrum distribution of $Y(2175) \to \phi(1020)\pi^{+} \pi^{-}$. Our calculation indicates there exist a sharp peak structure ($Z_{s1}^{+}$) close to the $K{\bar{K}}^{\ast }$ threshold and a broad structure ($Z_{s2}^{+}$) near the $K^{\ast }{\bar{K}}^{\ast }$ threshold. In addition, we also investigate the $\varphi (1680)\to \varphi (1020){\pi }^{+}{\pi }^{-}$ process due to the ISPE mechanism, where a sharp peak around the $K{\bar{K}}^{\ast }$ threshold appears in the $\varphi (1020){\pi }^{+}$ invariant mass spectrum distribution. We suggest to carry out the search for these charged strangeonium-like structures in future experiment, especially Belle II, Super-B and BESIII.