Infrared Anomalous Dimensions at Three-Loop in the SM from Conserved Currents

TL;DR

This paper calculates the infrared anomalous dimensions of the Standard Model's first-generation fermions at three-loop order, revealing new coupling-dependent terms in the cusp anomalous dimensions and providing comprehensive results for all gauge groups and particles.

Contribution

It presents the first three-loop calculation of infrared anomalous dimensions in the Standard Model, including novel coupling-dependent terms in the cusp anomalous dimensions.

Findings

Three-loop cusp anomalous dimensions include terms with two couplings.

Results are consistent with previous literature where comparisons are possible.

A comprehensive set of infrared anomalous dimensions for all particles and gauge groups is provided.

Abstract

We study the infrared structure of the Standard Model (SM) restricted to the first generation of fermions, including the full SM gauge group, up to three-loop order, and determine the resulting cusp and collinear anomalous dimensions for all gauge groups and particles of the theory. We observe that starting from three loops, the resulting cusp anomalous dimensions include terms involving two distinct couplings, contrary to previous claims in the literature. We give a detailed explanation of this observation and explore the origin of these terms. We provide a supplementary file where all infrared anomalous dimensions calculated in this work are collected. Our results are consistent with the existing literature wherever comparisons are possible.