Anomalous Dimension of a General Effective Gauge Theory II: Fermionic Sector

TL;DR

This paper derives the complete set of one-loop anomalous dimensions for the fermionic sector of general Effective Field Theories, enabling comprehensive renormalization group analysis of gauge EFTs with scalars and fermions.

Contribution

It provides the first full computation of fermionic anomalous dimensions in gauge EFTs, complementing previous bosonic results, and includes operator mixing and effects at order 1/Λ².

Findings

Complete one-loop anomalous dimensions for fermionic operators derived.

Operator mixing across dimensions included in the RGEs.

Results applicable to arbitrary gauge groups and non-renormalizable couplings.

Abstract

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.