Pion-induced production of theZc(3900)off a nuclear target

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We investigate the possibility to study the charmoniumlike state ${Z}_{c}(3900)$ through the pion-induced production off a nuclear target. By using a high-energy pion beam, the ${Z}_{c}(3900)$ can be produced off a proton or nucleus though the Primakoff effect. The production amplitude is calculated in an effective Lagrangian approach combined with the vector dominance model. The total cross sections of the $p({\ensuremath{\pi}}^{\ensuremath{-}},{Z}_{c}^{\ensuremath{-}}(3900))$ and $p({\ensuremath{\pi}}^{\ensuremath{-}},{Z}_{c}^{\ensuremath{-}}(3900)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{\ensuremath{-}})$ reactions are calculated, and their order of magnitude is about 0.1 and 0.01 nb, respectively, with an assumption of branch ratio 10% for the ${Z}_{c}(3900)$ decay in $J/\ensuremath{\psi}\ensuremath{\pi}$ channel. If the proton target is replaced by a nuclear target, the production of the ${Z}_{c}(3900)$ enhances obviously. The predicted total cross sections for the $A({\ensuremath{\pi}}^{\ensuremath{-}},{Z}_{c}^{\ensuremath{-}}(3900))$ and $A({\ensuremath{\pi}}^{\ensuremath{-}},{Z}_{c}^{\ensuremath{-}}(3900)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{\ensuremath{-}})$ reactions with $A=^{12}\mathrm{C}$ or $^{208}\mathrm{Pb}$ are on the order of magnitude of 100 and 10 nb, respectively, which is about one thousand times larger than the cross sections off a proton target. Based on these results, we suggest the experimental study of the ${Z}_{c}(3900)$ by using high-energy pion beams with a nuclear target at facilities such as COMPASS and J-PARC.