Structure of two-loop SMEFT anomalous dimensions via on-shell methods

TL;DR

This paper introduces on-shell techniques for calculating two-loop anomalous dimensions in SMEFT, providing a more efficient framework and verifying previous results, with implications for higher-order corrections in effective field theories.

Contribution

It presents a novel on-shell method for two-loop anomalous dimension calculations in SMEFT, improving computational efficiency and understanding of higher-order effects.

Findings

Verified existing one-loop SMEFT anomalous dimensions.

Identified conditions for vanishing two-loop anomalous terms.

Provided a framework for systematic two-loop computations.

Abstract

We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators. We also summarize methods for computing one-loop amplitudes, which are used as inputs to the computation of two-loop anomalous dimensions, and we explain how the structure of rational terms and judicious renormalization scheme choices can lead to additional vanishing terms in the anomalous dimension matrix at two loops. We describe the two-loop implications for the Standard Model Effective Field Theory (SMEFT). As a by-product of this analysis we verify a variety of one-loop SMEFT anomalous dimensions computed by Alonso, Jenkins, Manohar and Trott.