Partial-wave analysis of $ J/\psi \to \gamma \gamma \varphi $

Using a sample of $ \sim {10}^{10}\text{}\text{}J/\psi $ events collected by the BESIII detector at the BEPCII collider, a partial-wave analysis of the decay $ \gamma \gamma \varphi $ is performed to investigate the intermediate resonances in $ J/\psi \to \gamma R$, $ R\to \gamma \varphi $. 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/\psi \to \gamma R,R\to \gamma \varphi )$ are reported, and the resonance parameters of $ \eta (1405)$ and $ X(1835)$ have been precisely determined. It seems likely that $ \eta (1405)$ and $ X(1835)$ act as the first—and second—excited states of $ {\eta }^{\prime }$, respectively. The observation of $ {\eta }_{c}\to \gamma \varphi $ 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 branching fraction products do not conflict with theoretical expectations for X(2370) as a pseudoscalar glueball and $ {\eta }_{1}(1855)$ as a hybrid state.