Constraints for twist-two alien operators in QCD

A bstract 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.