Constraints on anomalous dimensions from the positivity of the S-matrix

TL;DR

This paper demonstrates how fundamental principles like analyticity, crossing symmetry, and the optical theorem constrain the evolution of higher-dimensional operators in effective field theories, revealing previously unrecognized zeros in the anomalous dimension matrix.

Contribution

It uncovers new constraints on anomalous dimensions derived from S-matrix properties, showing zeros in the matrix that were not previously known.

Findings

Identifies zeros in the anomalous dimension matrix due to S-matrix constraints

Provides a framework extendable to other effective field theories

Enhances understanding of RG evolution in the Standard Model EFT

Abstract

We show that the analyticity and crossing symmetry of the S-matrix, together with the optical theorem, impose restrictions on the renormalisation group evolution of dimension-eight operators in the Standard Model Effective Field Theory. Moreover, in the appropriate basis of operators, the latter manifest as zeros in the anomalous dimension matrix that, to the best of our knowledge, have not been anticipated anywhere else in the literature. Our results can be trivially extended to other effective field theories.