Collider Searches for Near-Continuum Dark Matter

We study collider constraints on the near-continuum dark matter model, in which the dark sector consists of a tower of closely spaced states with weak-scale masses coupled to the Standard Model through a $Z$-portal. To capture this structure in a model-agnostic way, we introduce a minimal parameterization that encodes the dominant geometric information with three parameters. Using a custom-built Monte-Carlo tool for near-continuous spectra, we simulate DM-pair production at $\sqrt{s}=13$ TeV and subsequent cascade decays via on/off-shell $Z$ bosons, which yield events with large missing transverse momentum and high jet multiplicity. Recasting the CMS multijet$+H_T^{\rm miss}$ analysis of Run-2 data (35.9 fb$^{-1}$), we derive bounds on the model parameter space. Extrapolating these bounds, we provide High-Luminosity LHC projections (3 ab$^{-1}$). We also project sensitivities for future electron-positron colliders at $\sqrt{s}=365$ GeV and $\sqrt{s}=500$ GeV, showing substantial improvements over the HL-LHC. The current LHC sensitivity is beginning to approach the theoretically motivated region of the parameter space, while future colliders will be able to comprehensively test this model.