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

In this work, we use the dispersion theory to provide a physical description of recent BESIII data on the reaction $e^+ e^- \to ψ(2S) \, π^+ \, π^-$. Taking into account explicitly the effects of charged exotic intermediate states in the $t$- and $u$-channels as well as the two-pion final state interaction, we describe the invariant mass distribution for four different $e^+ e^-$ center-of-mass energies. The effects of the $ππ$ rescattering are accounted for within a model-independent single channel approach which is found to explain the $ππ$-invariant mass distributions at all $e^+ e^-$ center-of-mass energies. For $q= 4.226$ GeV and $q= 4.258$ GeV the already established charged exotic state $Z_c(3900)$ is considered as the intermediate state, whereas for $q= 4.358$ GeV the rescattering of pions dominates the fits. For the highest energy, $q= 4.416$ GeV, a heavier charged exotic state with mass $m_{Z_c} = 4.016(4)$ GeV and width $Γ_{Z_c} = 52(10)$ MeV is essential to describe the experimental data. Although the mass of this state is consistent with the established $Z_c(4020)$, its width is significantly larger.

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