Measurement of the cross section of $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ at center-of-mass energies from 3.872 GeV to 4.700 GeV

Using data samples with an integrated luminosity of 19 fb${}^{-1}$ at twenty-eight center-of-mass energies from 3.872 GeV to 4.700 GeV collected with the BESIII detector at the BEPCII electron–positron collider, the process $e^{+}{e}^{-}\to \eta {\pi }^{+}{\pi }^{-}$ and the intermediate process $e^{+}{e}^{-}\to \eta {\rho }^0$ are studied for the first time. The Born cross sections are measured. No significant resonance structure is observed in the cross section lineshape.