Non-renormalization and operator mixing via on-shell methods

TL;DR

This paper introduces a new on-shell method-based non-renormalization theorem for operator mixing in massless 4D quantum field theories, revealing restrictions on operator renormalization and identifying zeros in anomalous-dimension matrices.

Contribution

It presents a general non-renormalization theorem for operator mixing using on-shell techniques, applicable to various operators in the Standard Model EFT, and explains zeros in anomalous-dimension matrices beyond previous helicity rules.

Findings

Operators of different lengths often do not mix at first order.

Zeros in anomalous-dimension matrices occur at multiple loops, beyond known helicity selection explanations.

Explicit two-loop calculations support the theorem's predictions.

Abstract

Using on-shell methods, we present a new perturbative non-renormalization theorem for operator mixing in massless four-dimensional quantum field theories. By examining how unitarity cuts of form factors encode anomalous dimensions we show that longer operators are often restricted from renormalizing shorter operators at the first order where there exist Feynman diagrams. The theorem applies quite generally and depends only on the field content of the operators involved. We apply our theorem to operators of dimension five through seven in the Standard Model Effective Field Theory, including examples of nontrivial zeros in the anomalous-dimension matrix at one through four loops. The zeros at two and higher loops go beyond those previously explained using helicity selection rules. We also include explicit sample calculations at two loops.