Measurement of the $\eta$ transition form factor through ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta$ decay

Abstract

Based on a sample of $(1.0087\pm 0.0044)\times 10^{10}$ $J/\psi$ events collected at BESIII, the transition form factor of the $\eta$ meson is extracted by analyzing $J/\psi \to \gamma {\eta }^{\prime },{\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta ,\eta \to \gamma l^{+}{l}^{-}$ ($l$=$e$, $\mu$) events. The measured slope of the transition form factor is ${\Lambda }^{-2}=1.645\pm 0.093_{stat.}\pm 0.024_{sys.}$ (GeV/$c^2$)${}^{-2}$ for the di-electron channel and ${\Lambda }^{-2}=1.645\pm 0.343_{stat.}\pm 0.017_{sys.}$ (GeV/$c^2$)${}^{-2}$ for the di-muon channel. The branching fractions for $\eta \to \gamma e^{+}{e}^{-}$ and $\eta \to \gamma {\mu }^{+}{\mu }^{-}$ are measured to be $\mathcal{B}(\eta \to \gamma e^{+}{e}^{-})=(6.79\pm 0.04_{stat.}\pm 0.36_{sys.})\times 10^{-3}$ and $\mathcal{B}(\eta \to \gamma {\mu }^{+}{\mu }^{-})=(2.97\pm 0.11_{stat.}\pm 0.07_{sys.})\times 10^{-4}$. 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 ${\Lambda }^{-2}=1.707\pm 0.076_{stat.}\pm 0.029_{sys.}$ (GeV/$c^2$)${}^{-2}$ and $\mathcal{B}(\eta \to \gamma e^{+}{e}^{-})=(6.93\pm 0.28_{tot.})\times 10^{-3}$. In addition, we search for the dark photon ($A^{\prime }$) using the combined events. No significant signal is observed, and the upper limits on $\mathcal{B}(\eta \to \gamma A^{\prime },A^{\prime }\to e^{+}{e}^{-})$ are set at 90\% confidence level for different $A^{\prime }$ mass hypotheses.

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