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In this work, we use the dispersion theory to provide a physical descriptionof recent BESIII data on the reaction $ e^+ e^- \to \psi (2S) \, \pi^+ \,\pi^-$. Taking into account explicitly the effects of charged exoticintermediate states in the $t$- and $u$-channels as well as the two-pion finalstate interaction, we describe the invariant mass distribution for fourdifferent $e^+ e^-$ center-of-mass energies. The effects of the $\pi\pi$rescattering are accounted for within a model-independent single channelapproach which is found to explain the $\pi \pi$-invariant mass distributionsat all $e^+ e^-$ center-of-mass energies. For $q= 4.226$ GeV and $q= 4.258$ GeVthe already established charged exotic state $Z_c(3900)$ is considered as theintermediate state, whereas for $q= 4.358$ GeV the rescattering of pionsdominates the fits. For the highest energy, $q= 4.416$ GeV, a heavier chargedexotic state with mass $m_{Z_c} = 4.016(4)$ GeV and width $\Gamma_{Z_c} =52(10)$ MeV is essential to describe the experimental data. Although the massof this state is consistent with the established $Z_c(4020)$, its width issignificantly larger.

The role of charged exotic states in $e^+e^- \to \psi(2S) \; \pi^+ \pi ^-$