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We use the framework of asymptotic safety above the Planck scale to constrainthe parameter space of simple models of new physics that can accommodate themeasured value of the anomalous magnetic moment of the muon and the relicdensity of dark matter. We couple parametrically to the trans-Planckian quantumphysics a set of SU(2)$\times$U(1) invariant extensions of the Standard Model,each comprising an inert scalar field and one pair of colorless fermions thatcommunicate to the muons through Yukawa-type interactions. The presence of aninteractive UV fixed point in the system of gauge and Yukawa couplings imposesa set of boundary conditions at the Planck scale, which allow one to deriveunique phenomenological predictions in each case and distinguish the differentrepresentations of the gauge group from one another. We apply to the modelsconstraints from the $h\to \mu\mu$ signal strength at ATLAS and CMS, direct LHCsearches for electroweak production with leptons and missing energy in thefinal state, and the dark matter relic density. We find that they furtherrestrict the available parameter space.

Minimal models for $g-2$ and dark matter confront asymptotic safety