Search for intermediate resonances and dark gauge bosons in $J/\psi \to \gamma {\pi }^{0}{\eta }^{\prime }$

We report on an analysis of the decay $J/\psi \to \gamma {\pi }^{0}{\eta }^{\prime }$ using a sample of $\left(1310.6±7.0\right)×{10}^{6}J/\psi $ events collected with the BESIII detector. We search for the $CP$-violating process ${\eta }_{c}\to {\pi }^{0}{\eta }^{\prime }$ and a dark gauge boson ${U}^{\prime }$ in $J/\psi \to {U}^{\prime }{\eta }^{\prime },{U}^{\prime }\to \gamma {\pi }^{0},{\pi }^{0}\to \gamma \gamma $. No evidence of an ${\eta }_{c}$ signal is observed in the ${\pi }^{0}{\eta }^{\prime }$ invariant-mass spectrum and the upper limit of the branching fraction is determined to be $5.6×{10}^{-5}$ at the 90% confidence level. We also find no evidence of ${U}^{\prime }$ production and set upper limits at the 90% confidence level on the product branching fraction $B\left(J/\psi \to {U}^{\prime }{\eta }^{\prime }\right)×B\left({U}^{\prime }\to {\pi }^{0}\gamma \right)$ in the range between $\left(0.8-6.5\right)×{10}^{-7}$ for $0.2\le {m}_{{U}^{\prime }}\le 2.1\text{}\text{}\mathrm{GeV}/{c}^{2}$. In addition, we study the process $J/\psi \to \omega {\eta }^{\prime }$ with $\omega \to \gamma {\pi }^{0}$. The branching fraction of $J/\psi \to \omega {\eta }^{\prime }$ is found to be $\left(1.87±0.09±0.12\right)×{10}^{-4}$, where the first uncertainty is statistical and the second is systematic, with a precision that is improved by a factor of 1.4 over the previously published BESIII measurement.