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


Gehrmann, Thomas; von Manteuffel, Andreas; Yang, Tong-Zhi (2023). Renormalization of twist-two operators in covariant gauge to three loops in QCD. Journal of High Energy Physics, 2023(4):41.

Abstract

Abstract
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.

Abstract

Abstract
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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Nuclear and High Energy Physics
Uncontrolled Keywords:Nuclear and High Energy Physics
Language:English
Date:11 April 2023
Deposited On:22 Dec 2023 12:49
Last Modified:09 Jul 2024 03:32
Publisher:Springer
ISSN:1029-8479
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/jhep04(2023)041
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)