One-loop Renormalization Group Equations in Generic Effective Field Theories. Part I: Bosonic Operators

TL;DR

This paper derives the one-loop Renormalization Group Equations for dimension-six bosonic operators in generic effective quantum field theories, providing foundational tools for future two-loop calculations in the Standard Model Effective Field Theory.

Contribution

It introduces a general method to compute one-loop RGEs for bosonic operators in theories with arbitrary gauge groups and scalar fields, laying groundwork for two-loop RGE derivations.

Findings

Derived one-loop RGEs for bosonic operators in generic EFTs.

Established a framework applicable to SMEFT and LEFT.

Paved the way for future two-loop RGE calculations.

Abstract

We consider a generic class of effective quantum field theories with arbitrary gauge groups and scalar matter fields. In such theories, we derive the one-loop Renormalization Group Equations (RGEs) for the physical dimension-six operators. The present paper is the first one in a series that is going to cover theories with spin-$\frac12$ matter fields, too, including the phenomenologically most relevant SMEFT and LEFT cases. Our present approach provides tools for deriving the yet unknown two-loop RGEs in the SMEFT.