The complete set of one-loop anomalous dimensions for general Effective Field Theories (EFTs) is derived using on-shell methods. Combined with previous findings for the bosonic sector, the obtained results conclude the computation of the complete set of leading order Renormalization Group Equations (RGEs) in arbitrary gauge EFTs containing scalar and fermion fields. Renormalization effects are consistently taken into account at the order $1/\Lambda^2$ in the new physics scale $\Lambda$ for all renormalizable and non-renormalizable couplings. The obtained template RGEs include operator mixing across different dimensions and are valid for arbitrary gauge groups.

We investigate the neutrino sector in the framework of flavor deconstruction with an inverse-seesaw realization. This setup naturally links the hierarchical charged-fermion masses to the anarchic pattern of light-neutrino mixing. We determine the viable parameter space consistent with oscillation data and study the phenomenology of heavy neutral leptons (HNL) and lepton-flavor-violating (LFV) processes. Current bounds from direct HNL searches and LFV decays constrain the right-handed neutrino scale to a few TeV, while future μ → e experiments will probe most of the region with Λ ≲ 10 TeV. Among possible realizations, models deconstructing SU(2)L × U(1)B−L or SU(2)L × U(1)R × U(1)B−L are those allowing the lowest deconstruction scale.

The future circular $e^+e^-$ collider (FCC-ee or CEPC) will provide unprecedented sensitivity to indirect new physics signals emerging as small deviations from the Standard Model predictions in electroweak precision tests. Assuming new physics scenarios containing a dark matter candidate and a $t$-channel mediator, we analyse the synergy and interplay of future Tera-$Z$ factories and non-collider tests conducted through direct and indirect searches of dark matter. Our results highlight the excellent prospect for a Tera-$Z$ run to indirectly probe the presence and nature of dark matter.

We point out that a QCD-like dark sector can be coupled to the Standard Model by gauging the topological Skyrme current, which measures the dark baryon number in the infrared, to give a technically natural model for dark matter. This coupling allows for a semi-annihilation process χχ → χXμ, where Xμ is the gauge boson mediator and χ a dark pion field, which plays the dominant role in setting the dark matter relic abundance. The topological interaction is purely p-wave and so free from indirect detection constraints. We show that the dark matter pion mass needs to be in the range 10 MeV ≲ mχ ≲ 1 TeV; towards the lighter end of this range, there can moreover be significant self-interactions. We discuss prospects for probing this scenario at collider experiments, ranging from the LHC to low-energy e+e− colliders, future Higgs factories, and beam-dump experiments.

We discuss a set of precision observables that can probe the existence of a light particle $X$ coupled to electrons in the mass range of 1-100 MeV. As a case study, we consider the recent excess of $e^+e^-$ final-state events at $\sqrt{s} = 16.9$ MeV reported by the PADME collaboration. Interestingly, this mass is tantalizingly close to the invariant mass at which anomalous $e^+e^-$ pair production has previously been observed in nuclear transitions from excited to ground states by the ATOMKI collaboration. For the scenario in which the new particle has a vector coupling to electrons, we show that the PADME excess is already in tension with constraints from the anomalous magnetic moment of the electron. Further improvements in the measurement of the electron $g$-2, together with upcoming results from PIONEER (searching for $\pi^+\to e^+ \nu X$) and Mu3e (searching for $\mu^+ \to e^+ \bar\nu_\mu\nu_e X$), are expected to definitively probe this scenario in the near future. We also explore alternative possibilities where the new particle has scalar, pseudoscalar, or axial-vector couplings.

We classify the physical operators of the most general bosonic effective gauge theory up to dimension six using on-shell methods. Based on this classification, we compute the complete one-loop anomalous dimension employing both on-shell unitarity-based and geometric techniques. Our analysis fully accounts for the mixing of operators with different dimensions. The results broadly apply to any Effective Field Theory with arbitrary gauge symmetry and bosonic degrees of freedom. To illustrate their utility, we perform a complete cross-check of results on the renormalization of the Standard Model Effective Field Theory (SMEFT), $O(n)$ scalar theory, and the SMEFT extended with an axion-like particle. Additionally, we present new results for axion-like particles with CP-violating interactions.