Partial wave analysis of $J/ψ\rightarrowγηη'$
Based on a sample of (10.09$\pm$0.04)$\times$10$^{9}$ $J/ψ$ events collected with the BESIII detector operating at the BEPCII storage ring, a partial wave analysis of the decay $J/ψ\rightarrow γηη'$ is performed. An isoscalar state with exotic quantum numbers $J^{PC}=1^{-+}$, denoted as $η_1(1855)$, has been observed for the first time with statistical significance larger than 19$σ$. Its mass and width are measured to be (1855$\pm$9$_{-1}^{+6}$)~MeV/$c^{2}$ and (188$\pm$18$_{-8}^{+3}$)~MeV, respectively. The product branching fraction ${\cal B}(J/ψ$$\rightarrow$$ γη_1(1855)$$\rightarrow$$γηη')$ is measured to be (2.70$\pm 0.41 _{-0.35}^{+0.16}) \times$10$^{-6}$. The first uncertainties are statistical and the second are systematic. In addition, an upper limit on the branching ratio ${\cal B}(f_0(1710)$$\rightarrow$$ηη')$/${\cal B}(f_0(1710)$$\rightarrow$$ππ)$ is determined to be $1.61 \times 10^{-3}$ at 90\% confidence level, which lends support to the hypothesis that the $f_0(1710)$ has a large glueball component.