Gluonic evanescent operators: two-loop anomalous dimensions

TL;DR

This paper computes the two-loop anomalous dimensions of evanescent operators in pure Yang-Mills theory, demonstrating their essential role and introducing an efficient method for high-dimensional operator renormalization.

Contribution

It presents the first calculation of two-loop anomalous dimensions for all dimension-10 operators using a novel combination of unitarity and tensor reduction techniques.

Findings

Two-loop anomalous dimensions are consistent across schemes at the Wilson-Fisher fixed point.

Evanescent operators are crucial for accurate two-loop renormalization.

The method improves efficiency in high-dimensional operator computations.

Abstract

Evanescent operators are a special class of operators that vanish in four-dimensional spacetime but are non-zero in $d=4-2\epsilon$ dimensions. In this paper, we continue our systematic study of the evanescent operators in the pure Yang-Mills theory and focus on their two-loop renormalization. We develop an efficient strategy to compute the two-loop divergences of form factors of high-dimensional and high-length operators by combining the $d$-dimensional unitarity method and the improved tensor reduction techniques. Two-loop anomalous dimensions are obtained for the mass-dimension-10 basis in the planar YM theory, for which both the $\overline{\text{MS}}$ scheme and the finite-renormalization scheme are used. We verify that the two-loop anomalous dimensions are the same in these two schemes at the Wilson-Fisher conformal fixed point. Our computation shows that the evanescent operators are indispensable in order to obtain the correct two-loop anomalous dimensions. This work provides a first computation of the two-loop anomalous dimensions of the complete set of dimension-10 operators. The method we use is also expected to provide an efficient strategy for the two-loop renormalization of general high-dimensional operators.