Origin of the near-degeneracy between the doublet and singlet masses

Determine the origin of the near equality between the vector-like doublet mass parameter $M_D$ and the singlet mass parameter $\mu$ required in the Majorana singlet–vector-like-doublet model for the LZ 248 keV event.

Background

The model explains the LZ event using a mostly singlet Majorana dark matter state mixed with a vector-like electroweak doublet. The relic abundance requires the doublet and singlet mass parameters to be highly degenerate: $M_D-\mu\lesssim0.2\,\mathrm{GeV}$ at the reference benchmark and approximately $10$–$95\,\mathrm{MeV}$ near the nominal solar-limit region.

The proposed ultraviolet completions discussed in the paper do not provide a common origin for these nearly equal masses. The unresolved issue is therefore a model-building explanation of the required mass relation, rather than a phenomenological constraint addressed by the paper.