Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector

TL;DR

This paper classifies operators in general bosonic effective gauge theories and computes their one-loop anomalous dimensions, providing a comprehensive framework applicable to various EFTs including SMEFT and axion-like particles.

Contribution

It introduces a complete classification of bosonic operators up to dimension six and calculates their one-loop anomalous dimensions using on-shell and geometric methods.

Findings

Validated results with SMEFT and scalar theories

Extended analysis to axion-like particles with CP violation

Provided a general approach for operator mixing and renormalization

Abstract

We classify the physical operators of the most general bosonic effective gauge theory up to dimension six using on-shell methods. Based on this classification, we compute the complete one-loop anomalous dimension employing both on-shell unitarity-based and geometric techniques. Our analysis fully accounts for the mixing of operators with different dimensions. The results broadly apply to any Effective Field Theory with arbitrary gauge symmetry and bosonic degrees of freedom. To illustrate their utility, we perform a complete cross-check of results on the renormalization of the Standard Model Effective Field Theory (SMEFT), $O(n)$ scalar theory, and the SMEFT extended with an axion-like particle. Additionally, we present new results for axion-like particles with CP-violating interactions.