Observation of $e^+ e^- to eta Y(2175)$ at center-of-mass energies above 3.7$sim$GeV

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