Anomalous Dimensions of Effective Theories from Partial Waves

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.

22 pages, 1 figure; v2: signs corrected and conventions clarified, other minor changes

References in corpus (3)

• Renormalization group coefficients and the S-matrix
• Two-Loop Renormalization of Quantum Gravity Simplified
• Operator Counting and Soft Blocks in Chiral Perturbation Theory

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• The Radial Action from Probe Amplitudes to All Orders
• Constructing the general partial waves and renormalization in EFT
• A Green's basis for the bosonic SMEFT to dimension 8