Observation of ${e}^{+}{e}^{-}\to \eta Y\left(2175\right)$ at center-of-mass energies above 3.7 GeV

The state $Y\left(2175\right)$ is observed in the process ${e}^{+}{e}^{-}\to \eta Y\left(2175\right)$ with a statistical significance larger than 10 standard deviations using the data collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energies between 3.7 and 4.6 GeV. This is the first observation of the $Y\left(2175\right)$ in this process. The mass and width of the $Y\left(2175\right)$ are determined to be $\left(2135±8±9\right)\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $\left(104±24±12\right)\text{}\text{}\mathrm{MeV}$, respectively, and the production cross section ($\sigma $) of ${e}^{+}{e}^{-}\to \eta Y\left(2175\right)\to \eta \varphi {f}_{0}\left(980\right)\to \eta \varphi {\pi }^{+}{\pi }^{-}$ is at the several hundred femtobarn level. No significant signal for the process ${e}^{+}{e}^{-}\to {\eta }^{\prime }Y\left(2175\right)$ is observed and the upper limit on $\sigma \left({e}^{+}{e}^{-}\to {\eta }^{\prime }Y\left(2175\right)\right)/\sigma \left({e}^{+}{e}^{-}\to \eta Y\left(2175\right)\right)$ is estimated to be 0.43 at the 90% confidence level. We also search for $\psi \left(3686\right)\to \eta Y\left(2175\right)$. No significant signal is observed, indicating a strong suppression relative to the corresponding $J/\psi $ decay, in violation of the "12% rule".