Study of $ \eta \to {\pi }^{+}{\pi }^{-}{l}^{+}{l}^{-}$

Using a sample of $ (10087\pm 44)\times {10}^{6}\text{}\text{}J/\psi $ events accumulated with the BESIII detector, we analyze the decays $ \eta \to {\pi }^{+}{\pi }^{-}{l}^{+}{l}^{-}$ ($ l=e$ or $ \mu $) via the process $ J/\psi \to \gamma \eta $. The branching fraction of $ \eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ is measured to be $ \mathcal{B}(\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-})=(3.07\pm 0.1{2}_{\mathrm{stat}}\pm 0.1{9}_{\mathrm{syst}})\times {10}^{-4}$. No signal events are observed for the $ \eta \to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ decay, leading to an upper limit on the branching fraction of $ \mathcal{B}(\eta \to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-})<4.0\times {10}^{-7}$ at the 90% confidence level. Furthermore, the $ CP$-violation asymmetry parameter is found to be $ {\mathcal{A}}_{CP}(\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-})=(-4.04\pm 4.6{9}_{\mathrm{stat}}\pm 0.1{4}_{\mathrm{syst}})\%$, showing no evidence of $ CP$-violation with current statistics. Additionally, we extract the transition form factor from the decay amplitude of $ \eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$. Finally, axionlike particles are searched for via the decay $ \eta \to {\pi }^{+}{\pi }^{-}a,a\to {e}^{+}{e}^{-}$, and upper limits on this branching fraction relative to that of $ \eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ are presented as a function of the axionlike particle mass in the range $ 5–200\text{}\text{}\mathrm{MeV}/{c}^{2}$.