Gluonic evanescent operators: classification and one-loop renormalization

TL;DR

This paper systematically classifies and computes one-loop renormalization of evanescent operators in pure Yang-Mills theory, revealing their potential impact on high-dimensional operators in effective field theories.

Contribution

It introduces a method to classify and construct d-dimensional evanescent operators in Yang-Mills theory and computes their one-loop anomalous dimensions.

Findings

Classified evanescent operators starting at mass dimension ten.

Computed one-loop form factors for these operators.

Determined their anomalous dimensions at one-loop.

Abstract

Evanescent operators are a special class of operators that vanish classically in four-dimensional spacetime, while in general dimensions they are non-zero and are expected to have non-trivial physical effects at the quantum loop level in dimensional regularization. In this paper we initiate the study of evanescent operators in pure Yang-Mills theory. We develop a systematic method for classifying and constructing the $d$-dimensional Lorentz invariant evanescent operators, which start to appear at mass dimension ten. We also compute one-loop form factors for the dimension-ten operators via the $d$-dimensional unitarity method and obtain their one-loop anomalous dimensions. These operators are necessary ingredients in the study of high dimensional operators in effective field theories involving a Yang-Mills sector.