Constraints for twist-two alien operators 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.

28 pages, LaTex, 4 figures, all-N results in ancillary Mathematica file, journal version

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Cited by in corpus (2)

• Combination of aN${}^3$LO PDFs and implications for Higgs production cross-sections at the LHC
• Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part