Leading Twist-Two Gauge-Variant Counterterms

TL;DR

This paper computes gauge-variant counterterms for twist-two operators in QCD, which are essential for understanding the scale evolution of parton distributions and contribute to higher-order calculations.

Contribution

It applies a novel method to calculate all gauge-variant one-loop counterterm Feynman rules with five legs, aiding four-loop splitting function computations.

Findings

Derived all gauge-variant counterterms needed for four-loop splitting functions.

Enhanced understanding of operator mixing in off-shell renormalization.

Facilitated higher-order QCD calculations with new Feynman rules.

Abstract

Anomalous dimensions of twist-two operators govern the scale evolution of parton distribution functions. For off-shell external states, the physical twist-two operators mix with unknown gauge-variant operators under renormalization. In this talk, we apply the method proposed by us in~\cite{Gehrmann:2023ksf} to compute all gauge-variant one-loop counterterm Feynman rules with five legs, which enter the determination of the four-loop splitting functions in QCD.