Renormalization of gluonic leading-twist operators in covariant gauges

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