Renormalization of gluonic leading-twist Operators in covariant Gauges

Abstract

We provide the all-loop structure of gauge-variant operators required for the renormalisation of Green's functions with insertions of twist-two operators in Yang-Mills theory. Using this structure we work out an explicit basis valid up to 4-loop order for an arbitrary compact simple gauge group. To achieve this we employ a generalised gauge symmetry, originally proposed by Dixon and Taylor, which arises after adding to the Yang-Mills Lagrangian also operators proportional to its equation of motion. Promoting this symmetry to a generalised BRST symmetry allows to generate the ghost operator from a single exact operator in the BRST-generalised sense. We show that our construction complies with the theorems by Joglekar and Lee. We further establish the existence of a generalised anti-BRST symmetry which we employ to derive non-trivial relations among the anomalous dimension matrices of ghost and equation-of-motion operators. For the purpose of demonstration we employ the formalism to compute the N=2,4 Mellin moments of the gluonic splitting function up to 4 loops and its N=6 Mellin moment up to 3 loops, where we also take advantage of additional simplifications of the background field formalism.

44 pages, 7 tables

References in corpus (14)

• New Relations for Gauge-Theory Amplitudes
• Higgs boson gluon-fusion production in N3LO QCD
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• Charged Current Drell-Yan Production at N3LO
• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements
• Low moments of the four-loop splitting functions in QCD
• Three-loop helicity amplitudes for diphoton production in gluon fusion
• The three-loop single mass polarized pure singlet operator matrix element
• Glue-and-Cut at Five Loops
• Renormalization and non-renormalization of scalar EFTs at higher orders