Search for the reaction channel ${e}^{+}{e}^{-}\to {\eta }_{c}\eta {\pi }^{+}{\pi }^{-}$ at center-of-mass energies from 4.23 to 4.60 GeV

Using data collected with the BESIII detector operating at the Beijing Electron Positron Collider, we search for the process ${e}^{+}{e}^{-}\to {\eta }_{c}\eta {\pi }^{+}{\pi }^{-}$. The search is performed using five large datasets recorded at center-of-mass energies of 4.23, 4.26, 4.36, 4.42, and 4.60 GeV. The ${\eta }_{c}$ meson is reconstructed in 16 exclusive decay modes. No signal is observed in the ${\eta }_{c}$ mass region at any center-of-mass energy. The upper limits on the reaction cross sections are determined to be 6.2, 10.8, 27.6, 22.6 and 23.7 pb at the 90% confidence level at the center-of-mass energies listed above.