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Search for intermediate resonances and dark gauge bosons in $J/ψ\rightarrowγπ^0η^{\prime}$

We report on an analysis of the decay $J/ψ\rightarrowγπ^0η^{\prime}$ using a sample of $(1310.6 \pm 7.0) \times ~10^6~ J/ψ$ events collected with the BESIII detector. We search for the CP-violating process $η_c\rightarrowπ^0η^{\prime}$ and a dark gauge boson $U'$ in $J/ψ\rightarrow U^{\prime}η^{\prime},~U^{\prime}\rightarrowγπ^0,~π^0\rightarrowγγ$. No evidence of an $η_{c}$ signal is observed in the $π^0η^{\prime}$ 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 $U'$ production and set upper limits at the 90\% confidence level on the product branching fraction $\mathcal{B}(J/ψ\rightarrow U^{\prime} η^{\prime}) \times \mathcal{B}(U^{\prime} \rightarrow π^{0} γ)$ in the range between $(0.8 - 6.5)\times 10^{-7}$ for 0.2 $\leq m_{U^{\prime}} \leq 2.1 $GeV$/c^{2}$. In addition, we study the process $J/ψ\rightarrowωη^{\prime}$ with $ω\rightarrowγπ^0$. The branching fraction of $J/ψ\rightarrowωη^{\prime}$ is found to be $(1.87\pm0.09\pm0.12) \times 10^{-4}$, 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.