Measurement of the η transition form factor through the η' → π⁺ π⁻ η decay

Based on a sample of (1.0087 ± 0.0044) × 10¹⁰ J/ψ events collected at BESIII, the transition form factor of the η meson is extracted by analyzing J/ψ → γη',η' → π⁺π⁻η and η → γl⁺l^- (l = e, μ) events. The measured slope of the transition form factor is Λ⁻² = 1.668 ± 0.093_stat ± 0.024_sys(GeV=/c²)⁻² for the di-electron channel and Λ⁻² = 1.645 ± 0.343_stat ± 0.017_sys(GeV/c²)⁻² for the di-muon channel. The branching fractions for η → γe⁺e⁻ and η → γμ⁺μ⁻ are measured to be B(η → γe⁺e⁻) = (6.79 ± 0.05_stat ± 0.36_sys) × 10⁻³ and B(η → γμ⁺μ⁻) = (2.97 ± 0.12_stat ± 0.07_sys) × 10⁻⁴. By combining with the results based on the J/ψ → γη and η → γe⁺e⁻ events from the previous BESIII measurement, we determine Λ⁻² = 1.707 ± 0.076_stat ± 0.029_sys(GeV/c²)⁻² and B(η → γe⁺e⁻) =(6.93 ± 0.28_tot) × 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 B(η → γA',A' → e⁺e⁻) are set at the 90% confidence level for different A' mass hypotheses.