Five-loop contributions to low-N non-singlet anomalous dimensions in QCD

Abstract

We present the first calculations of next-to-next-to-next-to-next-to-leading order (N^4LO) contributions to anomalous dimensions of spin-N twist-2 operators in perturbative QCD. Specifically, we have obtained the respective non-singlet quark-quark anomalous dimensions at N=2 and N=3 to the fifth order in the strong coupling alpha_s. These results set the scale for the N^4LO contributions to the evolution of the non-singlet quark distributions of hadrons outside the small-x region, and facilitate a first approximate determination of the five-loop cusp anomalous dimension. While the N^4LO coefficients are larger than expected from the lower-order results, their inclusion stabilizes the perturbative expansions for three or more light flavours at a sub-percent accuracy for alpha_s < 0.3.

arXiv comment11 pages, LaTeX, 2 figures. FORM file of the main results available with the source. v2: Nikhef and DESY numbers added, one very minor text modification. Version to appear in Phys. Lett. B

References in corpus (38)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• The four-loop beta-function in Quantum Chromodynamics
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Five-Loop Running of the QCD coupling constant
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• FORM version 4.0
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• Group theory factors for Feynman diagrams
• Revisiting parton evolution and the large-x limit
• Some higher moments of deep inelastic structure functions at next-to-next-to leading order of perturbative QCD
• On quartic colour factors in splitting functions and the gluon cusp anomalous dimension
• The strong coupling and its running to four loops in a minimal MOM scheme
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• Third-order QCD corrections to the charged-current structure function F_3
• Improved Approximations for the Three-Loop Splitting Functions in QCD
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering
• Four-loop QCD propagators and vertices with one vanishing external momentum
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• Scheme variations of the QCD coupling and hadronic $\tau$ decays
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Non-singlet structure functions beyond the next-to-next-to leading order
• Four loop anomalous dimension of the second moment of the non-singlet twist-2 operator in QCD
• Absence of pi^2 terms in physical anomalous dimensions in DIS: verification and resulting predictions
• Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams
• Renormalization group functions of QCD in the minimal MOM scheme
• Soft Resummation of Quark Anomalous Dimensions and Coefficient Functions in MS-bar Factorization
• Absence of even-integer $\zeta$-function values in Euclidean physical quantities in QCD
• Combinatorics of $\mathbf{R}$-, ${\mathbf{R}}^{-1}$-, and ${\mathbf{R}}^{\ast }$-operations and asymptotic expansions of feynman integrals in the limit of large momenta and masses
• Massless Propagators, $R(s)$ and Multiloop QCD
• Four loop anomalous dimension of the third and fourth moments of the non-singlet twist-2 operator in QCD
• First Forcer results on deep-inelastic scattering and related quantities
• On gamma_5 in higher-order QCD calculations and the NNLO evolution of the polarized valence distribution
• A planar four-loop form factor and cusp anomalous dimension in QCD
• R*-operation and five-loop calculations
• No-$\pi$ Theorem for Euclidean Massless Correlators

Cited by in corpus (35)

• The Large Hadron-Electron Collider at the HL-LHC
• 50 Years of Quantum Chromodynamics
• Collider Physics at the Precision Frontier
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• Fiducial Drell-Yan production at the LHC improved by transverse-momentum resummation at N${}^4$LL+N${}^3$LO
• The Four Loop QCD Rapidity Anomalous Dimension
• Low moments of the four-loop splitting functions in QCD
• Soft corrections to inclusive deep-inelastic scattering at four loops and beyond
• Approximate four-loop QCD corrections to the Higgs-boson production cross section
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators
• Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions
• From correlation functions to event shapes in QCD
• Projected transverse momentum resummation in top-antitop pair production at LHC
• Renormalization and non-renormalization of scalar EFTs at higher orders
• Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• The Hopf algebra structure of the $R^{\ast }$-operation
• Transcendental structure of multiloop massless correlators and anomalous dimensions
• Resummed inclusive cross-section in ADD model at N${}^3$LL+NNLO
• Gauge-invariant Renormalization of the Gluino-Glue operator
• Precision three-dimensional imaging of nuclei using recoil-free jets
• Thrust distribution in Higgs decays up to the fifth logarithmic order
• Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering
• OPITeR: A program for tensor reduction of multi-loop Feynman Integrals
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices
• NNLO anomalous dimension matrix for twist-two flavor-singlet operators
• Constraints for twist-two alien operators in QCD
• The $q_{\mathrm{T}}$ and $\Delta {\varphi }_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities
• Basis transformation properties of anomalous dimensions for hard exclusive processes
• Riemann $\zeta (4)$ function contributions to $O\left({{\alpha }_s}^5\right)$ terms of Adler D-function and Bjorken polarized sum rule in $SU\left(N_c\right)$ QCD: results and consequences
• Landau-Khalatnikov-Fradkin transformation and hatted zeta-values
• Three-Loop QCD corrections to the production of a Higgs boson and a Jet
• Renormalization of gluonic leading-twist Operators in covariant Gauges