Improved measurement of the branching fractions for $J/\psi \to \gamma {\pi }^{0}$, $\gamma \eta $, and $\gamma {\eta }^{\prime }$

Using a data sample of $\left(1.0087±0.0044\right)×{10}^{10}\text{}\text{}J/\psi $ events collected with the BESIII detector, the decays of $J/\psi \to \gamma {\pi }^{0}\left(\eta ,{\eta }^{\prime }\right)\to \gamma \gamma \gamma $ are studied. Newly measured branching fractions are $B\left(J/\psi \to \gamma {\pi }^{0}\right)=\phantom{\rule{0ex}{0ex}}\left(3.34±0.02±0.09\right)×{10}^{-5}$, $B\left(J/\psi \to \gamma \eta \right)=\left(1.096±0.001±0.019\right)×{10}^{-3}$, and $B\left(J/\psi \to \gamma {\eta }^{\prime }\right)=\phantom{\rule{0ex}{0ex}}\left(5.40±0.01±0.11\right)×{10}^{-3}$, where the first uncertainties are statistical and the second are systematic. These results are consistent with the world average values within two standard deviations. The ratio of partial widths $\Gamma \left(J/\psi \to \gamma {\eta }^{\prime }\right)/\Gamma \left(J/\psi \to \gamma \eta \right)$ is measured to be $4.93±0.13$. The singlet-octet pseudoscalar mixing angle ${\theta }_{P}$ is determined to be ${\theta }_{P}=-\left(22.11±0.26\right)°$ or $-\left(19.34±0.34\right)°$ with two different phenomenological models.