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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.
Original language | English |
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Article number | 177 |
Pages (from-to) | 1-43 |
Number of pages | 43 |
Journal | Journal of High Energy Physics |
Volume | 2022 |
Issue number | 5 |
DOIs | |
Publication status | Published - 26 May 2022 |
Keywords
- BRST Quantization
- Factorization
- Higher-Order Perturbative Calculations
- Renormalization Group
- Renormalization and Regularization
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Particle Theory at the Higgs Centre
Ball, R., Boyle, P., Del Debbio, L., Gardi, E., Horsley, R., Kennedy, A., O'Connell, D., Smillie, J. & Zwicky, R.
1/10/17 → 30/09/21
Project: Research