Scalar dark matter interpretation of the DAMPE data with U(1) gauge interactions

Recently, DAMPE experiment released the new measurement of the total cosmic $e^+e^-$ flux between 25 GeV and 4.6 TeV which indicates a spectral softening at around 0.9 TeV and a tentative peak at around 1.4 TeV. We utilize the scalar dark matter (DM) annihilation scenario to explain the DAMPE peak by extending $G_{SM}\equiv SU(3)_C \times SU(2)_L \times U(1)_Y$ with additional $U(1)$ gauge symmetries while keeping anomaly free to generate $\chi \chi \to Z^\prime Z^\prime \to \ell\bar{\ell}\ell^\prime\overline{\ell^\prime}$, where $\chi, Z^\prime, \ell^{(^\prime)}$ denote the scalar DM, the new gauge boson and $\ell^{(^\prime)}=e,\mu,\tau$, respectively, with $m_\chi \sim m_{Z^\prime} \sim 2 \times 1.5$ (TeV). We first illustrate that the minimal framework $G_{SM} \times U(1)_{Y^\prime}$ with the above mass choices can explain the DAMPE excess but has been excluded by LHC constraints from the $Z^\prime$ searches. Then we study a non-minimal framework $G_{SM} \times U(1)_{Y^\prime} \times U(1)_{Y^{\prime \prime}}$ in which $U(1)_{Y^{\prime \prime}}$ mixes with $U(1)_{Y^\prime}$. We show that such a framework can interpret the DAMPE data while passing other constraints including the DM relic abundance, DM direct detection and collider bounds. We also investigate the predicted $e^+e^-$ spectrum in this framework and find that the mass splitting $\Delta m = m_\chi - m_{Z'}$ should be less than about 17 GeV to produce the peak-like structure.