Measurement of the Electromagnetic Transition Form-factors in the decays $η'\rightarrowπ^+π^-l^+l^-$
With a sample of $(10087\pm44)\times10^{6}$ $J/ψ$ events accumulated with the BESIII detector, we analyze the decays $η'\rightarrowπ^+π^-l^+l^-(l=e,$ $μ)$ via the process $J/ψ\rightarrowγη'$. The branching fractions are measured to be $\mathcal{B}(η'\rightarrowπ^+π^-e^+e^-)=(2.45\pm0.02(\rm{stat.})\pm0.08(\rm{syst.})) \times10^{-3}$ and $\mathcal{B}(η'\rightarrowπ^+π^-μ^+μ^-)=(2.16\pm0.12(\rm{stat.})\pm0.06(\rm{syst.}))\times10^{-5}$, and the ratio is $\frac{\mathcal{B}(η'\rightarrowπ^{+}π^{-}e^{+}e^{-})}{\mathcal{B}(η'\rightarrowπ^{+}π^{-}μ^{+}μ^{-})} = 113.4\pm0.9(\rm{stat.})\pm3.7(\rm{syst.})$. In addition, by combining the $η'\rightarrowπ^+π^-e^+e^-$ and $η'\rightarrowπ^+π^-μ^+μ^-$ decays, the slope parameter of the electromagnetic transition form factor is measured to be $b_{η'}=1.30\pm0.19\ (\mathrm{GeV}/c^{2})^{-2}$, which is consistent with previous measurements from BESIII and theoretical predictions from the VMD model. The asymmetry in the angle between the $π^+π^-$ and $l^+l^-$ decay planes, which has the potential to reveal the $CP$-violation originating from an unconventional electric dipole transition, is also investigated. The asymmetry parameters are determined to be $\mathcal{A}_{CP}(η'\rightarrowπ^+π^-e^+e^-)=(-0.21\pm0.73(\rm{stat.})\pm0.01(\rm{syst.}))\%$ and $\mathcal{A}_{CP}(η'\rightarrowπ^+π^-μ^+μ^-)=(0.62\pm4.71(\rm{stat.})\pm0.08(\rm{syst.}))\%$, implying that no evidence of $CP$-violation is observed at the present statistics. Finally, an axion-like particle is searched for via the decay $η'\rightarrowπ^+π^-a, a\rightarrow e^+e^-$, and upper limits of the branching fractions are presented for the mass assumptions of the axion-like particle in the range of $0-500\ \mathrm{MeV}/c^{2}$.