Scalar dark matter with $Z_3$ symmetry in Type-II Seesaw

Abstract: We study a simple complex scalar singlet dark matter (DM) model with $Z_3$ symmetry in the framework of type-II seesaw mechanism. We use the model to explain the excess of electron-positron flux measured by AMS-02, DAMPE and Fermi-LAT collaborations, which is encouraged by the decay of the triplets produced from dark matter annihilations in the Galactic halo. We focus on the non-degenerate case in which the mass of DM is larger than that of the triplets' and deliberately alleviate the leptophilic properties of the DM, so that the semi-annihilation effects are enhanced. With the guarantee of $Z_3$ symmetry, by fitting the antiproton spectrum observed in PAMELA and AMS experiments, we find that the DM cubic terms and the couplings between DM and Higgs are strongly constrained, leading to the semi-annihilation cross section fraction less than $3\%$ when DM mass is given at 3 TeV.