Renormalization of general Effective Field Theories: Formalism and renormalization of bosonic operators

TL;DR

This paper develops a comprehensive formalism for the renormalization of general effective field theories involving scalars, fermions, and gauge bosons up to dimension 6, including basis construction and one-loop RG equations.

Contribution

It introduces a general framework for effective field theories with a basis construction and computes one-loop renormalization group equations for bosonic operators.

Findings

Established a Green and physical basis for the EFT

Derived one-loop RG equations for bosonic operators

Provided a systematic approach for EFT renormalization

Abstract

We describe the most general local, Lorentz-invariant, effective field theory of scalars, fermions and gauge bosons up to mass dimension 6. We first obtain both a Green and a physical basis for such an effective theory, together with the on-shell reduction of the former to the latter. We then proceed to compute the renormalization group equations for the bosonic operators of this general effective theory at one-loop order.