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In 2017, the BESIII Collaboration announced the observation of a chargedcharmonium-like structure in the $\psi(3686)\pi^\pm$ invariant mass spectrum ofthe $e^+ e^- \to \psi(3686) \pi^+ \pi^-$ process at different energy points,which enables us to perform a precise study of this process based on theinitial single pion emission (ISPE) mechanism. In this work, we perform acombined fit to the experimental data of the cross section of $e^+ e^- \to\psi(3686) \pi^+ \pi^-$, and the corresponding $\psi(3686)\pi^\pm$ and dipioninvariant mass spectra. Our result shows that the observed chargedcharmonium-like structure in $e^+ e^- \to \psi(3686) \pi^+ \pi^-$ can be wellreproduced based on the ISPE mechanism, and that the corresponding dipioninvariant mass spectrum and cross section can be depicted with the sameparameters. In fact, it provides strong evidence that the ISPE mechanism can bean underlying mechanism resulting in such novel a phenomenon.

Charged charmoniumlike structures in the $e^+ e^- \to \psi(3686) \pi^+ \pi^-$ process based on the ISPE mechanism