Search for the reaction channel $e^+ e^- \to ηη\,J/ψ$ and the isospin partner of the $Z_c(3900)$ at center-of-mass energies $\sqrt{s} = 4.226-4.950$ GeV
We search for the reaction channel $e^+ e^- \to ηη\,J/ψ$ in a data sample with center-of-mass energies from 4.226 to 4.950 GeV that was collected by the BESIII detector operating at the Beijing Electron Positron Collider (BEPCII). The data analysis is performed with two different reconstruction methods, exclusive and semi-inclusive, enabling a comparison and combination of the results. Only at a few energy points a non-zero cross section is observed with a statistical significance of more than 3$σ$ using one of the methods. Therefore, the corresponding upper limits of the cross section at the 90% confidence level are determined. The energy dependent results show clear deviations from the the line shape expected from three-body phase space alone. Since the statistical significance for almost all center-of-mass energies is low, the upper limits for the reaction channel $e^+ e^- \to ηη\,J/ψ$ also serve as limits for the existence of a possible isospin partner to the charmonium-like isospin triplet $Z_{\rm c}(3900)$ which decays to $J/ψη$.