Study of two-photon decays of pseudoscalar mesons via $J/\psi $ radiative decays

Using a sample of $4.48×{10}^{8}\text{}\text{}\psi \left(3686\right)$ events collected with the BESIII detector at the BEPCII collider, we study the two-photon decays of the pseudoscalar mesons ${\pi }^{0}$, $\eta $, ${\eta }^{\prime }$, $\eta \left(1405\right)$, $\eta \left(1475\right)$, $\eta \left(1760\right)$, and $X\left(1835\right)$ in $J/\psi $ radiative decays using $\psi \left(3686\right)\to {\pi }^{+}{\pi }^{-}J/\psi $ events. The ${\pi }^{0}$, $\eta $, and ${\eta }^{\prime }$ mesons are clearly observed in the two-photon mass spectra, and the branching fractions are determined to be $B\left(J/\psi \to \gamma {\pi }^{0}\to 3\gamma \right)=\left(3.57±0.12±0.16\right)×{10}^{-5}$, $B\left(J/\psi \to \gamma \eta \to 3\gamma \right)=\left(4.42±0.04±0.18\right)×{10}^{-4}$, and $B\left(J/\psi \to \gamma {\eta }^{\prime }\to 3\gamma \right)=\left(1.26±0.02±0.05\right)×{10}^{-4}$, where the first error is statistical and the second is systematic. No clear signal for $\eta \left(1405\right)$, $\eta \left(1475\right)$, $\eta \left(1760\right)$ or $X\left(1835\right)$ is observed in the two-photon mass spectra, and upper limits at the 90% confidence level on the product branching fractions are obtained.