Renormalization of general Effective Field Theories: Renormalization of fermionic operators

TL;DR

This paper completes the one-loop renormalization of general effective field theories up to dimension six by deriving beta functions for fermionic operators, enabling systematic renormalization using group theory.

Contribution

It provides the missing beta functions for fermionic operators, completing the one-loop renormalization framework for effective field theories up to dimension six.

Findings

Derived beta functions for fermionic operators at one loop.

Enabled renormalization of effective theories up to dimension six.

Facilitated group-theoretical calculations for EFT renormalization.

Abstract

Renormalization group equations play a central role in effective field theories, both maintaining perturbative control and allowing one to determine the correct low-energy phenomenology. In this work, we complete the one-loop renormalization of the recently developed general effective field theory up to mass dimension six by providing the beta functions for physical fermionic operators. Together with Ref. [1], our results allow one to renormalize any effective theory up to dimension six at one loop using only a group-theoretical calculation.