\begin{document}$ Z_x $\end{document} predicted by the \begin{document}$ U(1)_{L_e-L_\mu} $\end{document} model via the processes \begin{document}$ e^+e^-\rightarrow \ell^+\ell^-Z_x(Z_x\rightarrow \ell^+\ell^-) $\end{document} and \begin{document}$ e^+e^-\rightarrow \ell^+\ell^-Z_x(Z_x\rightarrow \nu_\ell\bar{\nu_\ell}) $\end{document} at the Circular Electron Positron Collider (CEPC) with a center of mass energy \begin{document}$ \sqrt s=240 $\end{document} GeV and luminosity \begin{document}$ \mathcal{L}=5.6 \;\; \mathrm{ab^{-1}} $\end{document}. We provide the expected sensitivities of the CEPC to the parameter space at the \begin{document}$ 1\sigma $\end{document}, \begin{document}$ 2\sigma $\end{document}, \begin{document}$ 3\sigma $\end{document}, and \begin{document}$ 5\sigma $\end{document} levels."> Searching for the light leptophilic gauge boson <i>Z</i><sub><i>x </i></sub>via four-lepton final states at the CEPC -
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