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

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