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

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 parto...

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Published inThe 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
LanguageEnglish
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
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Abstract 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.
AbstractList 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 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.
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.
ArticleNumber 41
Author Yang, Tong-Zhi
Gehrmann, Thomas
von Manteuffel, Andreas
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  givenname: Andreas
  surname: von Manteuffel
  fullname: von Manteuffel, Andreas
  organization: Department of Physics and Astronomy, Michigan State University
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  givenname: Tong-Zhi
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  surname: Yang
  fullname: Yang, Tong-Zhi
  email: toyang@physik.uzh.ch
  organization: Physik-Institut, Universität Zürich, Department of Physics and Astronomy, Michigan State University
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CitedBy_id crossref_primary_10_1103_PhysRevD_108_034027
crossref_primary_10_1140_epjc_s10052_024_13071_3
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Snippet A bstract The leading short-distance contributions to hadronic hard-scattering cross sections in the operator product expansion are described by twist-two...
The leading short-distance contributions to hadronic hard-scattering cross sections in the operator product expansion are described by twist-two quark and...
Abstract The leading short-distance contributions to hadronic hard-scattering cross sections in the operator product expansion are described by twist-two quark...
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StartPage 41
SubjectTerms 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
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Title Renormalization of twist-two operators in covariant gauge to three loops in QCD
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