We investigate the minimal $U(1{)}_{L_{\mu }-L_{\tau }}$ model with extra heavy vectorlike leptons or charged scalars. By studying the kinetic mixing between $U(1{)}_{L_{\mu }-L_{\tau }}$ gauge boson $Z^{\prime }$ and standard model photon, which is absent at tree level and will arise at one-loop level due to $\mu$, $\tau$, and new heavy charged leptons or scalars, the interesting behavior is shown. It can provide the possibility for visible signatures of new heavy particles. We propose to search for $Z^{\prime }$ at electron collider experiments, such as Belle II, BESIII, and future Super Tau Charm Factory (STCF), using the monophoton final state. The parameter space of $Z^{\prime }$ is probed and scanned by its gauge coupling constant $g_{Z^{\prime }}$ and mass $m_{Z^{\prime }}$. We find that electron colliders have sensitivity to the previously unexplored parameter space for $Z^{\prime }$ with MeV–GeV mass. Future STCF experiments with $\sqrt{s}=2–7\mathrm{GeV}$ can exclude the anomalous muon magnetic moment favored area when $m_{Z^{\prime }}<5\mathrm{GeV}$ with the luminosity of $30{\mathrm{ab}}^{-1}$. For $m_{Z^{\prime }}<2m_{\mu }$, $g_{Z^{\prime }}$ can be down to $4.2\times {10}^{-5}$ at 2 GeV STCF.

• Received 21 September 2020
• Accepted 16 December 2020

DOI:https://doi.org/10.1103/PhysRevD.103.015008

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Published by the American Physical Society