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Constraining $U(1)_{L_μ-L_τ}$ 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$σ$ discrepancy compared with the expectation of the Standard Model \cite{Fermi_Lab}. A new light gauge boson $X$ in the $L_μ-L_τ$ model provides a good explanation for the $g-2$ anomaly. A Dirac fermion dark matter with a large $L_μ-L_τ$ 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. $m_Ψ > m_μ$) for which the channel $ΨΨ\rightarrow μ^- μ^+$ opens. Although the cross section $(σv)_{μ^{-}μ^{+}}$ is smaller by a factor of $1/q_Ψ^2$ ($q_Ψ$ represents the $L_μ-L_τ$ charge of the dark matter) compared with the channel $ΨΨ\rightarrow XX \rightarrow νν\barν\barν$, 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 $ΨΨ\rightarrow μ^{-}μ^{+}$, which rules out part of the parameter space of the large $L_μ-L_τ$ charged dark matter model to account for the muon $g-2$ anomaly.