Anomalous Dimensions of Effective Theories from Partial Waves

TL;DR

This paper introduces a method using angular momentum decomposition to efficiently compute one-loop anomalous dimensions in effective theories, including the Standard Model EFT, nonlinear sigma models, and gravity.

Contribution

It develops a partial wave approach to simplify the calculation of anomalous dimensions, extending on-shell amplitude methods to a broader class of theories.

Findings

Reduced one-loop anomalous dimension calculations to sums of partial wave products.

Derived a generic formula for nonlinear sigma models' anomalous dimensions.

Demonstrated the method's effectiveness in gravity despite IR divergences.

Abstract

On-shell amplitude methods have proven to be extremely efficient for calculating anomalous dimensions. We further elaborate on these methods to show that, by the use of an angular momentum decomposition, the one-loop anomalous dimensions can be reduced to essentially a sum of products of partial waves. We apply this to the SM EFT, and show how certain classes of anomalous dimensions have their origin in the same partial-wave coefficients. We also use our result to obtain a generic formula for the one-loop anomalous dimensions of nonlinear sigma models at any order in the energy expansion, and apply our method to gravity, where it proves to be very advantageous even in the presence of IR divergencies.