Measurement of the cross sections for $e^+e^-\to\eta\pi^+\pi^-$ at center-of-mass energies between 2.00 and 3.08 GeV

Using data samples collected at center-of-mass energies between 2.000 and 3.080 GeV with the BESIII detector operating at the BEPCII collider, a partial-wave analysis is performed on the process $e^+e^-\to\eta\pi^+\pi^-$. In addition to the dominant $e^+e^-\to\rho\eta$ component, the $e^+e^-\to a_2(1320)\pi$ process is also sizeable, contributing up to 24% of the total reaction. The measured cross sections of the process $e^+e^-\to\eta\pi^+\pi^-$ are systematically higher than those of BaBar by more than $3\sigma$ at center-of-mass energies between 2.000 and 2.300 GeV. In the cross section lineshape for $e^+e^-\to a_2(1320)\pi$, a resonant structure is observed with a significance of $5.5\sigma$, with $M=(2044\pm31\pm4)$ MeV/$c^2$, $\Gamma=(163\pm69\pm24)$ MeV and $\mathcal{B_{R}}\cdot\Gamma_{e^+e^-}^{R}=(34.6\pm17.1\pm6.0)$ eV or $(137.1\pm73.3\pm2.1)$ eV. In the cross section lineshape for $e^+e^-\to\rho\eta$, an evidence of a dip structure around 2180 MeV/$c^2$ is observed with statistical significance of $3.0\sigma$.