Constraining $U(1{)}_{L_{\hat{I}}¼-L_{\ddot{I}}„}$ charged dark matter model for muon $g-2$ anomaly with AMS-02 electron and positron data

Abstract

Very recently, the Fermi-Lab reported the new experimental combined results on the magnetic momentum of muon with a 4.2$\ddot{I}ƒ$ discrepancy compared with the expectation of the Standard Model \cite{Fermi_Lab}. A new light gauge boson $X$ in the $L_{\hat{I}}¼-L_{\ddot{I}}„$ model provides a good explanation for the $g-2$ anomaly. A Dirac fermion dark matter with a large $L_{\hat{I}}¼-L_{\ddot{I}}„$ 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. $m_{\hat{I}}¨>m_{\hat{I}}¼$) for which the channel $\hat{I}¨\hat{I}¨\to \hat{I}{¼}^{-}\hat{I}{¼}^{+}$ opens. Although the cross section $(\ddot{I}ƒv{)}_{\hat{I}{¼}^{-}\hat{I}{¼}^{+}}$ is smaller by a factor of $1/q_{\hat{I}}{¨}^2$ ($q_{\hat{I}}¨$ represents the $L_{\hat{I}}¼-L_{\ddot{I}}„$ charge of the dark matter) compared with the channel $\hat{I}¨\hat{I}¨\to XX\to \hat{I}½\hat{I}½\bar{\hat{I}}½\bar{\hat{I}}½$, 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 $\hat{I}¨\hat{I}¨\to \hat{I}{¼}^{-}\hat{I}{¼}^{+}$, which rules out part of the parameter space of the large $L_{\hat{I}}¼-L_{\ddot{I}}„$ charged dark matter model to account for the muon $g-2$ anomaly.

5 pages,3 figures