The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order

Abstract

We report a new result for the $N_f{C}_F^3$ contribution to the four-loop anomalous dimensions of non-singlet, twist-two operators in Quantum Chromodynamics. This result is obtained through computations of off-shell operator matrix elements. Employing integration-by-parts reductions and differential equations with respect to a tracing parameter allowed us to derive analytic results valid for arbitrary Mellin moment $n$.

arXiv comment13 pages, 1 figure, ancillary file with result, journal version

References in corpus (54)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Higgs boson gluon-fusion production in N3LO QCD
• Harmonic sums, Mellin transforms and Integrals
• Harmonic Sums and Mellin Transforms up to two-loop Order
• A novel approach to integration by parts reduction
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Renormalization and Running of Quark Mass and Field in the Regularization Invariant and MS-bar Schemes at Three and Four Loops
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• Revisiting parton evolution and the large-x limit
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• The Drell-Yan cross section to third order in the strong coupling constant
• Soft-/rapidity- anomalous dimensions correspondence
• Anomalous dimensions of high-spin operators beyond the leading order
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
• Collider Physics at the Precision Frontier
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• $Apart: A Generalized Mathematica Apart Function
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• Approximate N${}^3$LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN${}^3$LO PDFs
• Transforming differential equations of multi-loop Feynman integrals into canonical form
• Libra: a package for transformation of differential systems for multiloop integrals
• Iterated Binomial Sums and their Associated Iterated Integrals
• Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements
• The Four Loop QCD Rapidity Anomalous Dimension
• The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements
• The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,N_F)}$
• Four-loop collinear anomalous dimensions in QCD and $\mathcal{N}=4$ super Yang-Mills
• The toolbox of modern multi-loop calculations: novel analytic and semi-analytic techniques
• Soft corrections to inclusive deep-inelastic scattering at four loops and beyond
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• $\text{tapir}$: A tool for topologies, amplitudes, partial fraction decomposition and input for reductions
• The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements
• Four-loop splitting functions in QCD -- The quark-quark case
• Absence of pi^2 terms in physical anomalous dimensions in DIS: verification and resulting predictions
• Anomalous dimensions of operators in polarized deep inelastic scattering at O(1/N_f)
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• Planar master integrals for four-loop form factors
• The inverse Mellin transform via analytic continuation
• Renormalization of twist-two operators in covariant gauge to three loops in QCD

Cited by in corpus (7)

• Scaling violation in power corrections to energy correlators from the light-ray OPE
• disorder: Deep inelastic scattering at high orders
• Constraints for twist-two alien operators in QCD
• Combination of aN${}^3$LO PDFs and implications for Higgs production cross-sections at the LHC
• Benchmark of deep-inelastic-scattering structure functions at $\mathcal{O}({\alpha }_s^3)$
• Anomalous dimensions at small spins
• Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part