Observation and study of the decay $J/\psi \to \varphi \eta {\eta }^{\prime }$

We report the observation and study of the decay $J/\psi \to \varphi \eta {\eta }^{\prime }$ using $1.3×1{0}^{9}$ $J/\psi $ events collected with the BESIII detector. Its branching fraction, including all possible intermediate states, is measured to be $\left(2.32±0.06±0.16\right)×{10}^{-4}$. We also report evidence for a structure, denoted as $X$, in the $\varphi {\eta }^{\prime }$ mass spectrum in the $2.0–2.1\text{}\text{}\mathrm{GeV}/{c}^{2}$ region. Using two decay modes of the ${\eta }^{\prime }$ meson ($\gamma {\pi }^{+}{\pi }^{-}$ and $\eta {\pi }^{+}{\pi }^{-}$), a simultaneous fit to the $\varphi {\eta }^{\prime }$ mass spectra is performed. Assuming the quantum numbers of the $X$ to be ${J}^{P}={1}^{-}$, its significance is found to be $4.4\sigma $, with a mass and width of $\left(2002.1±27.5±21.4\right)\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $\left(129±17±9\right)\text{}\text{}\mathrm{MeV}$, respectively, and a product branching fraction $B\left(J/\psi \to \eta X\right)×B\left(X\to \varphi {\eta }^{\prime }\right)=\left(9.8±1.2±1.7\right)×{10}^{-5}$. Alternatively, assuming ${J}^{P}={1}^{+}$, the significance is $3.8\sigma $, with a mass and width of $\left(2062.8±13.1±7.2\right)\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $\left(177±36±35\right)\text{}\text{}\mathrm{MeV}$, respectively, and a product branching fraction $B\left(J/\psi \to \eta X\right)×\phantom{\rule{0ex}{0ex}}B\left(X\to \varphi {\eta }^{\prime }\right)=\left(9.6±1.4±2.0\right)×{10}^{-5}$. The angular distribution of $J/\psi \to \eta X$ is studied and the two ${J}^{P}$ assumptions of the $X$ cannot be clearly distinguished due to the limited statistics. In all measurements the first uncertainties are statistical and the second systematic.