Constraints for twist-two alien operators in QCD

TL;DR

This paper systematically studies alien operators in QCD twist-two sectors at arbitrary spin, deriving their couplings and Feynman rules using generalized BRST symmetry, and provides one-loop results for operator renormalization up to four loops.

Contribution

It introduces a systematic method to analyze alien operators at any spin in QCD using generalized BRST symmetry and provides explicit one-loop results for renormalization.

Findings

Derived all couplings of alien operators with gluons at arbitrary spin.

Established relations between alien operator couplings with different gluon numbers.

Provided necessary one-loop results for four-loop operator renormalization in QCD.

Abstract

Parton evolution equations in QCD are controlled by the anomalous dimensions of gauge-invariant twist-two spin-$N$ quark and gluon operators. Under renormalization, these mix with gauge-variant operators of the same quantum numbers, referred to as alien operators. Our work addresses the systematic study of these alien operators at arbitrary spin $N$, using generalized BRST symmetry relations to derive their couplings and Feynman rules at all values of $N$. We observe how the all-$N$ structure of the generalized (anti-)BRST constraints relates the couplings of alien operators with $n+1$ gluons to those with $n$ gluons. Realizing a bootstrap, we present all one-loop results necessary for performing the operator renormalization up to four loops in QCD.