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.
Highlights
Effective Field Theory (EFT) approaches have risen to prominence in recent years as a systematic means for quantifying new physics beyond the Standard Model
We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators
First we summarize the results of our previous paper, which points out a set of nontrivial zeros in the two-loop anomalous dimension matrix of generic EFTs [10]: operators with longer length — those with more field insertions — are often restricted from renormalizing operators with shorter length, even if Feynman diagrams exist
Summary
Effective Field Theory (EFT) approaches have risen to prominence in recent years as a systematic means for quantifying new physics beyond the Standard Model. We apply on-shell methods to identify a new set of vanishing terms in the two-loop anomalous dimension matrix of the SMEFT. Using the unitarity-based formalism, we find that many potential contributions to the two-loop anomalous dimension matrix vanish for a variety of reasons, including the appearance of only scaleless integrals [10], color selection rules, vanishing rational terms at one loop, as well as appropriate renormalization scheme choices at one loop. These vanishing contributions go beyond those identified in our previous paper [10]. The explicit D-dimensional forms of the full one-loop amplitudes, as well as their four-dimensional finite remainders, are relegated to the Supplementary material and appendix B, respectively
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