Renormalization of effective field theories via on-shell methods: the case of axion-like particles

TL;DR

This paper develops a novel on-shell method to compute the renormalization group equations for general axion-like particle effective field theories, simplifying calculations and clarifying operator relations.

Contribution

It introduces on-shell and unitarity-based techniques to evaluate RGEs in axion-like theories, extending previous results and improving computational efficiency.

Findings

On-shell methods simplify RGE calculations.

Double-cut integration via Stokes' theorem is effective.

Explicit verification of operator duality under CP symmetry.

Abstract

We consider the most general axion-like particle effective field theory, including both CP-odd and CP-even types of interactions, and evaluate the corresponding renormalization group equations, improving and extending previous results in the literature. Our calculations exploit on-shell and unitarity-based methods. The relevant phase-space cut-integrals are carried out using different integration methods, among which the double-cut integration via Stokes' theorem proves to be technically simpler. A close comparison between the standard Feynman diagrammatic approach and the unitarity-based method enables us to explicitly verify the reduction of complexity in the latter case, along with a more direct and elegant way to establish a connection among anomalous dimensions of operators that are dual under the CP symmetry.