Renormalization of twist-two operators in QCD and its application to singlet splitting functions

TL;DR

This paper introduces a new method for extracting Feynman rules from off-shell operator matrix elements in QCD, enabling independent calculation of three-loop singlet splitting functions related to parton evolution.

Contribution

The authors develop a novel systematic approach to derive Feynman rules for gauge-variant operators without prior knowledge, applied here to reproduce known three-loop singlet splitting functions.

Findings

Successfully reproduce three-loop singlet splitting functions

Develop a new method for extracting Feynman rules from off-shell operators

Enhance understanding of operator mixing in QCD renormalization

Abstract

Splitting functions govern the scale evolution of parton distribution functions. Through a Mellin transformation, they are related to anomalous dimensions of twist-two operators in the operator product expansion. We study off-shell operator matrix element, where the physical operators mix under renormalization with other gauge-variant operators of the same quantum numbers. We devise a new method to systematically extract the Feynman rules resulting from those operators without knowing the operators themselves. As a first application of the new approach, we independently reproduce the well-known three-loop singlet splitting functions obtained from computations of on-shell quantities.