Minimal Scale-Invariant Dark Matter

Abstract

We study the minimal classically scale-invariant extension of the Standard Model, containing a single $\mathbb Z_2$-stabilised real scalar singlet whose mass is not an independent input but is generated dynamically through the quantum effective potential and linked to radiative electroweak symmetry breaking through the Higgs portal. We construct the full two-field one-loop effective potential and introduce a modified on-shell renormalisation scheme that fixes the electroweak vacuum, the Higgs mass, the vanishing Higgs--singlet mixing and the singlet curvature at the physical point, yielding predictions stable under renormalisation-scale variation. Since thermal freeze-out is excluded by direct-detection limits, we identify a highly predictive freeze-in realisation of this model. Imposing perturbativity, vacuum stability and the observed relic abundance leads to a freeze-in solution with a dark-matter mass of around $2~{\rm MeV}$. The predicted electron-scattering cross section for this solution lies far below the current sensitivity of DAMIC-M. Current direct-detection experiments therefore do not constrain this scenario. The minimal scale-invariant singlet model thus provides a robust and highly predictive framework connecting radiative electroweak symmetry breaking and freeze-in dark-matter genesis.