Observation of an Axial-Vector State in the Study of the Decay $ \psi (3686)\to \varphi \eta {\eta }^{\prime }$

Using $ (2712.4\pm 14.3)\times {10}^{6}$ $ \psi (3686)$ events collected with the BESIII detector at BEPCII, a partial wave analysis of the decay $ \psi (3686)\to \varphi \eta {\eta }^{\prime }$ is performed with the covariant tensor approach. In addition to the established states $ {h}_{1}(1900$) and $ \varphi (2170)$, an axial-vector state with a mass near $ 2.3\text{}\text{}\mathrm{GeV}/{c}^{2}$ is observed for the first time. Its mass and width are measured to be $ 2316\pm {9}_{\mathrm{stat}}\pm 3{0}_{\mathrm{syst}}\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $ 89\pm 1{5}_{\mathrm{stat}}\pm 2{6}_{\mathrm{syst}}\text{}\text{}\mathrm{MeV}$, respectively. The product branching fractions of $ \mathcal{B}[\psi (3686)\to X(2300){\eta }^{\prime }]\mathcal{B}[X(2300)\to \varphi \eta ]$ and $ \mathcal{B}[\psi (3686)\to X(2300)\eta ]\mathcal{B}[X(2300)\to \varphi {\eta }^{\prime }]$ are determined to be $ (4.8\pm {1.3}_{\mathrm{stat}}\pm {0.7}_{\mathrm{syst}})\times {10}^{-6}$ and $ (2.2\pm {0.7}_{\mathrm{stat}}\pm {0.7}_{\mathrm{syst}})\times {10}^{-6}$, respectively. The branching fraction $ \mathcal{B}[\psi (3686)\to \varphi \eta {\eta }^{\prime }]$ is measured for the first time to be ($ 3.14\pm 0.1{7}_{\mathrm{stat}}\pm 0.2{4}_{\mathrm{syst}})\times {10}^{-5}$. The first uncertainties are statistical and the second are systematic.