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

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