Search for an isoscalar partner of the $Z_c(3900)$ in $e^+e^-\toπ^+π^-ηJ/ψ$
Using a data sample corresponding to an integrated luminosity of 20.3 fb$^{-1}$ collected at center-of-mass energies from 4.18 to 4.95 GeV with the BESIII detector, we observe the process $e^+e^-\toπ^+π^-ηJ/ψ$ with a statistical significance of $6.0 σ$, including systematic uncertainties. The isoscalar partner of the $Z_c(3900)$, denoted $X(3900)$, is searched for in the $ηJ/ψ$ final state, and no significant signal is observed. The upper limits on the product of the Born cross section $σ^{\rm Born}[e^{+}e^{-}\toπ^{+}π^{-} X(3900)$] and the branching fraction $\mathcal{B}[X(3900)\toηJ/ψ]$ are given with various assumptions for the mass and width of the $X(3900)$.