Inert sextuplet scalar dark matter at the LHC and future colliders

We study a dark matter model constructed by extending the standard model with an inert $\mathrm{SU}(2)_\mathrm{L}$ sextuplet scalar of hypercharge 1/2. The sextuplet components are split by the quartic couplings between the sextuplet and the Higgs doublet after electroweak symmetry breaking, resulting in a dark sector with one triply charged, two doubly charged, two singly charged, and two neutral scalars. The lighter neutral scalar boson acts as a dark matter particle. We investigate the constraints on this model from the $\text{monojet} + /\!\!\!\!E_\mathrm{T}$ and $\text{soft-dilepton} + \text{jets} + /\!\!\!\!E_\mathrm{T}$ searches at the 13 TeV Large Hadron Collider, as well as from the current electroweak precision test. Furthermore, we estimate the projected sensitivities of a 100 TeV $pp$ collider and of a future $e^+e^-$ collider, and find that such future projects could probe TeV mass scales. Nonetheless, such mass scales only correspond to a subdominant component of the observed relic abundance if the dark matter particles solely originate from thermal production.