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

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 $1\mathrm{/}{\mathrm{\Lambda }}^2$ in the new physics scale $\mathrm{\Lambda }$ for all renormalizable and non-renormalizable couplings. The obtained template RGEs include operator mixing across different dimensions and are valid for arbitrary gauge groups.