Leptophilic dark matter in gauged $U(1{)}_{L_e-L_{\mu }}$ model in light of DAMPE cosmic ray $e^{+}+e^{-}$ excess

Motivated by the very recent cosmic-ray electron+positron excess observed by DAMPE collaboration, we investigate a Dirac fermion dark matter (DM) in the gauged $L_e-L_{\mu }$ model. DM interacts with the electron and muon via the $U(1{)}_{e-\mu }$ gauge boson $Z^{{}^{\mathrm{\prime }}}$. The model can explain the DAMPE data well. Although a non-zero DM-nucleon cross section is only generated at one loop level and there is a partial cancellation between $Z^{{}^{\mathrm{\prime }}}ee$ and $Z^{{}^{\mathrm{\prime }}}\mu \mu$ couplings, we find that a large portion of $Z^{{}^{\mathrm{\prime }}}$ mass is ruled out from direct DM detection limit leaving the allowed $Z^{{}^{\mathrm{\prime }}}$ mass to be close to two times of the DM mass. Implications for $pp\to Z^{{}^{\mathrm{\prime }}}\to 2\mathrm{\ell }$ and $pp \to 2\ell + Z^{'}$,andmuon$g-2$ anomaly are also studied.