Renormalization of twist-two operators in covariant gauge to three loops in QCD

• Published in: The journal of high energy physics Vol. 2023; no. 4; pp. 41 - 62
• Main Authors: Gehrmann, Thomas, von Manteuffel, Andreas, Yang, Tong-Zhi
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 11.04.2023; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Deep Inelastic Scattering or Small-x Physics; Distribution functions; Elementary Particles; Gluons; High energy physics; Higher-Order Perturbative Calculations; Mathematical analysis; Operators (mathematics); Partons; Physics; Physics and Astronomy; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum numbers; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; Renormalization and Regularization; Scattering cross sections; String Theory; Renormalization and Regularization; Deep Inelastic Scattering or Small-x Physics; Higher-Order Perturbative Calculations
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2023)041

A bstract The leading short-distance contributions to hadronic hard-scattering cross sections in the operator product expansion are described by twist-two quark and gluon operators. The anomalous dimensions of these operators determine the splitting functions that govern the scale evolution of parton distribution functions. In massless QCD, these anomalous dimensions can be determined through the calculation of off-shell operator matrix elements, typically performed in a covariant gauge, where the physical operators mix with gauge-variant operators of the same quantum numbers. We derive a new method to systematically extract the counterterm Feynman rules resulting from these gauge-variant operators. As a first application of the new method, we rederive the unpolarized three-loop singlet anomalous dimensions, independently confirming previous results obtained with other methods. Employing a general covariant gauge, we observe the explicit cancellation of the gauge parameter dependence in these results.