The energy-dependent cross section for
e+e−→ηψ(2S) is measured at 18 center of mass energies from 4.288 to 4.951 GeV using the BESIII detector. Using the same data samples, we also perform the first search for the reaction
e+e−→ηX˜(3872), but no evidence is found for the
X˜(3872) in the
π+π−J/ψ mass distribution. At each of the 18 center of mass energies, upper limits at the 90% confidence level on the cross section for
e+e−→ηψ(2S) and on the product of the
e+e−→ηX˜(3872) cross section with the branching fraction of
X˜(3872)→π+π−J/ψ are reported. Published by the American Physical Society 2024