Scalar dark matter, Type II Seesaw and the DAMPE cosmic ray $e^+ + e^-$ excess.

The DArk Matter Particle Explorer (DAMPE) has reported a measurement of the flux of high energy cosmic ray electrons plus positrons (CREs) in the energy range between $25$ GeV and $4.6$ TeV. With unprecedented high energy resolution, the DAMPE data exhibit an excess of the CREs flux at an energy of around $1.4$ TeV. In this letter, we discuss how the observed excess can be understood in a minimal framework where the Standard Model (SM) is supplemented by a stable SM singlet scalar as dark matter (DM) and type II seesaw for generating the neutrino mass matrix. In our framework, a pair of DM particles annihilates into a pair of the SM SU(2) triplet scalars ($\Delta$s) in type II seesaw, and the subsequent $\Delta$ decays create the primary source of the excessive CREs around $1.4$ TeV. The lepton flavor structure of the primary source of CREs has a direct relationship with the neutrino oscillation data. We find that the DM interpretation of the DAMPE excess determines the pattern of neutrino mass spectrum to be the inverted hierarchy type, taking into account the constraints from the Fermi-LAT observations of dwarf spheroidal galaxies.