Partial Wave Analysis of $J\mathrm{/}\psi \to \gamma \gamma \phi$

Using a sample of $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected by the BESIII detector at the BEPCII collider, a partial-wave analysis of the decay $\gamma \gamma \phi$ is performed to investigate the intermediate resonances in $J\mathrm{/}\psi \to \gamma R,R\text{ar}\gamma \phi$. Resonances including $f_1(1285)$, $\eta (1405)$, $f_1(1420)$, $f_1(1510)$, $f_2(1525)$, $X(1835)$, $f_2(1950)$, $f_2(2010)$, $f_0(2200)$ and ${\eta }_c$ have been detected with statistical significance greater than 5$\sigma$. The product branching fractions $\mathcal{B}(J\mathrm{/}\psi \to \gamma R,R\text{ar}\gamma \phi )$ are reported, and the resonance parameters of $\eta (1405)$ and $X(1835)$ have been precisely determined. It is more probable that $\eta (1405)$ and $X(1835)$ act as the first - and second - excited states of ${\eta }^{\mathrm{\prime }}$, respectively. The observation of ${\eta }_c\to \gamma \phi$ holds great significance for the in depth study of charmonium properties. No evidence of $\eta (1295)$, ${\eta }_1(1855)$ or X(2370) is found. The measured upper limits of relevant BF products do not conflict with theoretical expectations for X(2370) as a pseudoscalar glueball and ${\eta }_1(1855)$ as a hybrid state.