Cross section measurement of 𝑒+⁢𝑒−→𝜂⁢𝜓⁡(2⁢𝑆) and search for 𝑒+⁢𝑒−→𝜂⁢ ˜𝑋 ⁢(3872)

The energy-dependent cross section for 𝑒+⁢𝑒−→𝜂⁢𝜓⁡(2⁢𝑆) 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−→𝜂⁢˜𝑋⁡(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−→𝜂⁢𝜓⁡(2⁢𝑆) and on the product of the 𝑒+⁢𝑒−→𝜂⁢˜𝑋⁡(3872) cross section with the branching fraction of ˜𝑋⁡(3872)→𝜋+⁢𝜋−⁢𝐽/𝜓 are reported.