Constraining $U(1{)}_{L_{\mu }-L_{\tau }}$ charged dark matter model for muon $g-2$ anomaly with AMS-02 electron and positron data

Very recently, the Fermi-Lab reported the new experimental combined results on the magnetic momentum of muon with a 4.2$\sigma$ discrepancy compared with the expectation of the Standard Model \cite{Fermi_Lab}. A new light gauge boson $X$ in the $L_{\mu }-L_{\tau }$ model provides a good explanation for the $g-2$ anomaly. A Dirac fermion dark matter with a large $L_{\mu }-L_{\tau }$ charge can explain both the $g-2$ anomaly and the dark matter relic density \cite{Asai_2021}. In this work, we focus on the case that the mass of the dark matter is larger than the mass of muon (i.e. $m_{\mathrm{\Psi }}>m_{\mu }$) for which the channel $\mathrm{\Psi }\mathrm{\Psi }\to {\mu }^{-}{\mu }^{+}$ opens. Although the cross section $(\sigma v{)}_{{\mu }^{-}{\mu }^{+}}$ is smaller by a factor of $1\mathrm{/}{q}_{\mathrm{\Psi }}^2$ ($q_{\mathrm{\Psi }}$ represents the $L_{\mu }-L_{\tau }$ charge of the dark matter) compared with the channel $\Psi\Psi \rightarrow XX \rightarrow \nu\nu\bar{\nu}\bar{\nu}$, the resulting secondary electrons and positrons could imprint on their spectra above GeV energies due to the reacceleration effect of cosmic ray propagation. We use the AMS-02 measurements of electrons and positrons to constrain the annihilation cross section of the channel $\mathrm{\Psi }\mathrm{\Psi }\to {\mu }^{-}{\mu }^{+}$, which rules out part of the parameter space of the large $L_{\mu }-L_{\tau }$ charged dark matter model to account for the muon $g-2$ anomaly.