Theoretical and experimental constraints on $$\mathbb {Z}_{2n}$$ multi-component dark matter models

Abstract 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 $$\mathbb {Z}_{2n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:math> symmetries, specifically the $$\mathbb {Z}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> , $$\mathbb {Z}_6(23)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>23</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , and $$\mathbb {Z}_6(13)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>13</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> 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 $$\mathbb {Z}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> model offers a broadly viable parameter space sustained by efficient semi-annihilation. In stark contrast, the $$\mathbb {Z}_6(13)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>13</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> scenario is shown to be highly fine-tuned, with solutions confined to the Higgs resonance. Our most significant finding concerns the $$\mathbb {Z}_6(23)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>23</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> 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 $$10^6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>6</mml:mn> </mml:msup> </mml:math> GeV scale. This work provides a definitive guide to the viability of these $$\mathbb {Z}_{2n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:math> scenarios and serves as a compelling demonstration of how high-energy consistency checks can yield crucial insights into the nature of dark matter.