Anomalous Dimensions, Matching, and Phenomenology of Dirac Fermionic Dark Matter Effective Interactions

Abstract

We explore a fermionic dark matter (DM) extension of the Standard Model Effective Field Theory (SMEFT) and establish a complete renormalisation-group framework for its phenomenological investigation. We derive the anomalous-dimension matrix of all relevant dimension-five and dimension-six operators involving Standard Model (SM) and DM fields, enabling the consistent evolution of the associated Wilson coefficients (WCs) across energy scales. By combining renormalisation-group running with matching at the relevant thresholds, we construct a robust bridge between high-scale new physics and experimental observables. We then perform a comprehensive phenomenological analysis, evaluating the contributions of these operators to observables spanning a wide range of energies and deriving constraints on the WCs from current data. We obtain stringent and complementary bounds on the DM effective field theory (DMEFT) WCs from electroweak precision observables, flavour processes, lepton-flavour-violating decays, top-quark flavour-changing neutral-current decays, and invisible meson decays. Interpreted in terms of the effective scale of new physics, the resulting limits demonstrate that current precision measurements probe energy scales ranging from the TeV regime to several tens or even hundreds of TeV, highlighting the remarkable sensitivity of indirect searches to dark-sector interactions.