The three-loop QCD $\beta$-function and anomalous dimensions

Abstract

The analytic calculation of the three-loop QCD $\beta$-function and anomalous dimensions within the minimal subtraction scheme in an arbitrary covariant guage is presented. The result for the $\beta$-function coincides with the previous calculation \cite{tvz}.

5 pages, NIKHEF-H/92-17

References in corpus (1)

• QCD Perturbation Theory at Low Energies

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• Evolution of the spin of the nucleon
• Threshold Resummation Effects in Neutral Higgs Boson Production by Bottom Quark Fusion at the CERN Large Hadron Collider
• Four-loop critical properties of polymerized membranes
• The DIS 1-Jettiness Event Shape at N${}^3$LL+$\mathcal{O}({\alpha }_s^2)$
• The scalar glueball operator, the a-theorem, and the onset of conformality
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• The photon energy spectrum in $B\to X_s\gamma$ at N${}^3$LL${}^{\prime }$
• Renormalization scheme dependence of high-Order perturbative QCD predictions
• QCD and QED renormalization group functions - a large N_f approach
• $Z$-boson hadronic decay width up to $\mathcal{O}({\alpha }_s^4)$-order QCD corrections using the single-scale approach of the principle of maximum conformality
• Benchmark of deep-inelastic-scattering structure functions at $\mathcal{O}({\alpha }_s^3)$
• NNLO QCD corrections to the resonant sneutrino/slepton production at Hadron Colliders
• Bilinear quark operator renormalization at generalized symmetric point
• Angularity in Higgs boson decays via $\mathbf{H}\to \mathbf{gg}$ at NNLL${}^{\prime }$ accuracy
• Five loop renormalization of the Wess-Zumino model
• New constraints on the up-quark valence distribution in the proton
• Next-to-next-to-leading order fits to CCFR'97 $x{F}_3$ data and infrared renormalons
• On the Scale Variation of the Total Cross Section for Higgs Production at the LHC and at the Tevatron
• Small-momentum expansion of heavy-quark correlators in the large-${\beta }_0$ limit and ${\alpha }_s$ extractions
• Higgs Decay, Z Decay and the QCD Beta-Function
• Nontrivial, Asymptotically Non-free Gauge Theories and Dynamical Unification of Couplings
• Reanalysis of the top-quark pair production via the $e^{+}{e}^{-}$ annihilation near the threshold region up to N${}^3$LO QCD corrections
• Anomalous Dimensions at an Infrared Fixed Point in an SU($N_c$) Gauge Theory with Fermions in the Fundamental and Antisymmetric Tensor Representations
• PartonDensity.jl: a novel parton density determination code
• Operator product expansion for the non-local gluon condensate
• Structure function evolution at next-to-leading order and beyond
• Three loop MSbar renormalization of QED in the 't~Hooft-Veltman gauge
• Non-perturbative decoupling of massive fermions
• Gauge-invariant approach to the beta function in Yang-Mills theories with universal extra dimensions
• Parton densities and structure functions beyond the next-to-leading order
• The Banks-Zaks expansion in perturbative QCD: an update
• Three-loop jet function for boosted heavy quarks
• Six dimensional ultraviolet completion of the $CP(N)$ $\sigma$ model at two loops
• Towards a Two-Loop Matching of Gauge Couplings in Grand Unified Theories
• Method for comparing finite temperature field theory results with lattice data
• Transmutation of Scale Dependence into Truncation Uncertainty via RG-Improvement of the $R(s)$ Series
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• Approximate N${}^5$LO Higgs boson decay width $\Gamma (H\to \gamma \gamma )$
• Generalized symmetry constraints on deformed 4d (S)CFTs
• Three loop MSbar anomalous dimension for renormalizable gauge invariant non-local gluon mass operator in QCD
• Symmetric point flavour singlet axial vector current renormalization at two loops
• The Higgs-Boson Decay $H\to gg$ to Order ${\alpha }_s^5$ under the mMOM-Scheme
• One-loop triple collinear splitting amplitudes in QCD
• Off-shell quark bilinear operator Green's functions at two loops
• Parton distributions in the virtual photon target up to NNLO in QCD
• The Standard Model from the LHC to future colliders: a contribution to the Workshop "What Next" of INFN
• Three-Loop QCD corrections to the production of a Higgs boson and a Jet
• A Gribov equation for the photon Green's function
• Hadronic and radiative decays of the tau lepton
• Effective Field Theories for the LHC
• QCD analysis of $x{F}_3$ structure functions in deep-inelastic scattering: Mellin transform by Gegenbauer polynomial up to N${}^3$LO approximation
• At the Frontier of Precision QCD in the LHC Era
• Matching QCD and HQET at three loops
• Three loop QCD corrections to heavy quark form factors
• Soft Integrals and Soft Anomalous Dimensions at N${}^3$LO and Beyond
• Higgs boson decay into heavy quarks and heavy leptons: higher order corrections
• One-to-One correspondence of soft and hard Pomeron with the CDP of the gluon density at low $x$
• Contraction and decomposition matrices for vacuum diagrams
• Parameter Inference from Final-State Entanglement in Higgs Decays
• Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics
• Renormalisation
• Slepton pair production with aNNLO+NNLL precision
• Perturbative QCD fitting of KEDR and BESIII $e^{+}{e}^{-}$ data for R(s) and ${\alpha }_s$ determination
• One-loop matching for quark dipole operators in a gradient-flow scheme
• Spiral Multi-component Structure in Pade - Approximant QCD
• Do we need Feynman diagrams for higher orders perturbation theory?
• Determination of the b-mass using renormalon cancellation
• An optimal scheme for top quark mass measurement near $t\bar{t}$ threshold at future $e^{+}{e}^{-}$ colliders