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

We report on an analysis of the decay $J\mathrm{/}\psi \to \gamma {\pi }^0{\eta }^{\mathrm{\prime }}$ using a sample of $(1310.6 \pm 7.0) \times ~10^6~ J/\psi$ events collected with the BESIII detector. We search for the CP-violating process ${\eta }_c\to {\pi }^0{\eta }^{\mathrm{\prime }}$ and a dark gauge boson $U^{\mathrm{\prime }}$ in $J/\psi\rightarrow U^{\prime}\eta^{\prime},~U^{\prime}\rightarrow\gamma\pi^0,~\pi^0\rightarrow\gamma\gamma$. No evidence of an ${\eta }_c$ signal is observed in the ${\pi }^0{\eta }^{\mathrm{\prime }}$ invariant-mass spectrum and the upper limit of the branching fraction is determined to be $7.2\times {10}^{-5}$ at the 90% confidence level. We also find no evidence of $U^{\mathrm{\prime }}$ production and set upper limits at the 90% confidence level on the product branching fraction $$\mathcal{B}$(J/\psi \rightarrow U^{\prime} \eta^{\prime}) \times $\mathcal{B}$(U^{\prime} \rightarrow \pi^{0} \gamma)$intherangebetween$(0.8 - 6.5)\times 10^{-7}$for0.2$\leq m_{U^{\prime}} \leq 2.1 $GeV$/c^{2}$\mathrm{.}Inaddition,westudytheprocess$J/\psi\rightarrow\omega\eta^{\prime}$with$\omega\rightarrow\gamma\pi^0$. The branching fraction of $J\mathrm{/}\psi \to \omega {\eta }^{\mathrm{\prime }}$ is found to be $(1.87\pm 0.09\pm 0.12)\times {10}^{-4}$, 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.