On equations of motion in twist-four evolution

TL;DR

This paper analyzes the renormalization of twist-four operators in QCD, focusing on operator mixing with equations of motion, and confirms previous results through an alternative approach avoiding explicit Feynman diagram calculations.

Contribution

It provides a detailed analysis of operator mixing with equations of motion in twist-four evolution, complementing prior diagrammatic calculations in QCD.

Findings

Confirmed earlier evolution equations for twist-four operators

Clarified the role of equations of motion in operator mixing

Validated results without explicit Feynman graph analysis

Abstract

Explicit diagrammatic calculation of evolution equations for high-twist correlation functions is a challenge already at one-loop order in QCD coupling. The main complication being quite involved mixing pattern of the so-called non-quasipartonic operators. Recently, this task was completed in the literature for twist-four nonsinglet sector. Presently, we elaborate on a particular component of renormalization corresponding to the mixing of gauge-invariant operators with QCD equations of motion. These provide an intrinsic contribution to evolution equations yielding total result in agreement with earlier computations that bypassed explicit analysis of Feynman graphs.