Partial wave analysis of $J/\psi \to \gamma \eta {\eta }^{\prime }$

Based on a sample of $\left(10.09±0.04\right)×{10}^{9}$ $J/\psi $ events collected with the BESIII detector operating at the BEPCII storage ring, a partial wave analysis of the decay $J/\psi \to \gamma \eta {\eta }^{\prime }$ is performed. An isoscalar state with exotic quantum numbers ${J}^{PC}={1}^{-+}$, denoted as ${\eta }_{1}\left(1855\right)$, has been observed for the first time with statistical significance larger than $19\sigma $. Its mass and width are measured to be $\left(1855±{9}_{-1}^{+6}\right)\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $\left(188±{18}_{-8}^{+3}\right)\text{}\text{}\mathrm{MeV}$, respectively. The first uncertainties are statistical and the second are systematic. The product branching fraction $B\left(J/\psi \to \gamma {\eta }_{1}\left(1855\right)\right)B\left({\eta }_{1}\left(1855\right)\to \eta {\eta }^{\prime }\right)$ is measured to be $\left(2.70±{0.41}_{-0.35}^{+0.16}\right)×{10}^{-6}$. In addition, an upper limit on the ratio of branching fractions $B\left({f}_{0}\left(1710\right)\to \eta {\eta }^{\prime }\right)/B\left({f}_{0}\left(1710\right)\to \pi \pi \right)$ is determined to be $1.61×{10}^{-3}$ at 90% confidence level, which lends support to the hypothesis that the ${f}_{0}\left(1710\right)$ has a large glueball component.