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

Abstract

Using a sample of $(10087\pm 44)\times 10^6$ $J/\psi$ 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 $\mathcal{B}(\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-})=(3.07\pm 0.12_{stat.}\pm 0.19_{syst.})\times 10^{-4}$. 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 ${\mathcal{A}}_{CP}(\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-})=(-4.04\pm 4.69_{stat.}\pm 0.14_{syst.})\%$, 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, axion-like 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 axion-like particle mass in the range $5-200\mathrm{MeV}/c^2$.

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