Theoretical and Experimental Constraints on $\mathbb{Z}_{2n}$ Multi-Component Dark Matter Models

A complete assessment of any dark matter model requires confronting its low-energy phenomenology with its high-scale theoretical viability. We undertake such a dual analysis for a class of two-component scalar dark matter models stabilized by $\mathbb{Z}_{2n}$ symmetries, specifically the $\mathbb{Z}_4$, $\mathbb{Z}_6(23)$, and $\mathbb{Z}_6(13)$ frameworks. Each model is tested against the latest observational data, including the Planck relic abundance and stringent direct detection limits from the LUX-ZEPLIN (LZ) experiment. Simultaneously, we evaluate their theoretical integrity up to the GUT and Planck scales by enforcing vacuum stability and perturbative unitarity with one-loop Renormalization Group Equations. This combined approach reveals a rich and varied landscape of possibilities. We demonstrate that the $\mathbb{Z}_4$ model offers a broadly viable parameter space sustained by efficient semi-annihilation. In stark contrast, the $\mathbb{Z}_6(13)$ scenario is shown to be highly fine-tuned, with solutions confined to the Higgs resonance. Our most significant finding concerns the $\mathbb{Z}_6(23)$ model: we show that an apparent conflict between experimental data and high-scale consistency is resolved when the model is viewed as an effective field theory, yielding a concrete prediction for new physics at or below the $10^6$ GeV scale. This work provides a definitive guide to the viability of these $\mathbb{Z}_{2n}$ scenarios and serves as a compelling demonstration of how high-energy consistency checks can yield crucial insights into the nature of dark matter.