Prospects of type-II seesaw at future colliders in light of the DAMPE $e^{+}{e}^{-}$ excess

The DAMPE $e^{+}{e}^{-}$ excess at around 1.4 TeV could be explained in the type-II seesaw model with a scalar dark mater $D$ which is stabilized by a discrete $Z_2$ symmetry. The simplest scenario is the annihilation $DD \to H^{++} H^{–}$followedbythesubsequentdecay$H^{\pm\pm} \to e^\pm e^\pm$, with both the DM and triplet scalars roughly 3 TeV with a small mass splitting. In addition to the Drell-Yan process at future 100 TeV hadron colliders, the doubly-charged components could also be produced at lepton colliders like ILC and CLIC in the off-shell mode, and mediate lepton flavor violating processes $e^{+}{e}^{-}\to {\mathrm{\ell }}_i^{\pm }{\mathrm{\ell }}_j^{\mp }$ (with $i\mathrm{\ne }j$). A wide range of parameter space of the type-II seesaw could be probed, which are well below the current stringent lepton flavor constraints.