Based on a sample of $(1.0087\pm0.0044)\times10^{ 10}$ $J/\psi$ events collected at BESIII, the transition form factor of the $\eta$ meson is extracted by analyzing $J/\psi\to\gamma\eta',~\eta'\to\pi^+\pi^-\eta,~\eta\to\gamma l^+l^-$ ($l$=$e$, $\mu$) events. The measured slope of the transition form factor is $\Lambda^{ -2}=1.645\pm0.093_{ \rm stat.}\pm { 0.024_{ \rm sys.}}$ (GeV/$c^2$)$^{ -2}$ for the di-electron channel and $\Lambda^{ -2}=1.645\pm0.343_{ \rm stat.}\pm0.017_{ \rm sys.}$ (GeV/$c^2$)$^{ -2}$ for the di-muon channel. The branching fractions for $\eta\rightarrow\gamma e^+e^-$ and $\eta\rightarrow\gamma\mu^+\mu^-$ are measured to be $\mathcal{ B}(\eta\to\gamma e^+e^-)=(6.79\pm0.04_{ \rm stat.}\pm0.36_{ \rm sys.})\times 10^{ -3}$ and $\mathcal{ B}(\eta\to\gamma\mu^+\mu^-)=(2.97\pm0.11_{ \rm stat.}\pm0.07_{ \rm sys.})\times 10^{ -4}$. By combining with the results based on the $J/\psi\to\gamma\eta,~\eta\to\gamma e^+e^-$ events from the previous BESIII measurement, we determine $\Lambda^{ -2}=1.707\pm0.076_{ \rm stat.}\pm0.029_{ \rm sys.}$ (GeV/$c^2$)$^{ -2}$ and $\mathcal{ B}(\eta\to\gamma e^+e^-)=(6.93\pm0.28_{ \rm tot.})\times 10^{ -3}$. In addition, we search for the dark photon ($A'$) using the combined events. No significant signal is observed, and the upper limits on $\mathcal{ B}(\eta\to\gamma A',~A'\to e^+e^-)$ are set at 90\% confidence level for different $A'$ mass hypotheses.
Categories: hep-ex