The four-loop β-function in quantum chromodynamics

Ritbergen, T. van; Vermaseren, J.A.M.; Larin, S.A.

doi:10.1016/s0370-2693(97)00370-5

Cited by 1,088 publications

(1,277 citation statements)

References 20 publications

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“…Finally, at finite N , the series are clearly asymptotic, the 1/N 2 terms in (2.12,2.13) (the result of the first divergent non-planar contribution -which appears at four loops [38]) having a much larger coefficient (and of the same sign). Without further information (see below), we can estimate the sums only in the cases where this last term is not the smallest term.…”

Section: Renormalizability In Extra Dimensionsmentioning

confidence: 90%

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Renormalizable extra-dimensional models

Morris

2005

J. High Energy Phys.

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Non-Abelian gauge theories may have continuum limits in more than four dimensions, supported by non-trivial ultra-violet fixed points. Moreover, such theories can be expected to be accessible to Wilson's epsilon expansion. We investigate this series for SU (N ) Yang-Mills, in particular for the fixed point coupling and exponent ν, up to four loops. From the model-building point of view, such theories would be effectively perturbatively renormalizable in the normal way. A particularly attractive possibility is the construction of renormalizable extra-dimensional models of the weak interactions, which have the potential to address the full hierarchy problem. The simplest such gauge-Higgs unification model is however ruled out by a combination of theoretical and phenomenological constraints.

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Section: Renormalizability In Extra Dimensionsmentioning

confidence: 90%

“…We then review the evidence such as it is for higher dimensional fixed points. After this we use the known four-loop four-dimensional beta function [37,38] to investigate the ǫ expansion for these fixed points. (It seems that this is the first time the early two-loop investigation [23] has been extended.…”

Section: Introductionmentioning

confidence: 99%

Renormalizable extra-dimensional models

Morris

2005

J. High Energy Phys.

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“…both with perturbatively calculable coefficients known to N 3 LO, see [27] for the beta-function coefficients and [28,29] for the mass anomalous dimension γ q . Another popular scheme for heavy-quark masses is the so-called on-shell scheme, where the pole-mass m q is chosen to coincide with the pole of the heavy-quark propagator at each order in perturbative QCD.…”

Section: Non-perturbative Parametersmentioning

confidence: 99%

Status of perturbative QCD calculations for deep-inelastic scattering and related processes

Moch¹

2012

Nuclear Physics B - Proceedings Supplements

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We give a brief overview of the status of perturbative QCD calculations for deep-inelastic scattering. The radiative corrections to the Wilson coefficients are generally available to next-to-next-to-leading order in QCD and we address the accuracy of the strong coupling constant, the parton distributions of the nucleon and the heavy quark masses which is required for precision predictions. We also discuss related processes at hadron colliders such as Higgs production via weak boson fusion which can be described through structure functions of deep-inelastic scattering, building upon an approximate, although very accurate, factorization of the perturbative QCD corrections. Keywords: Deep-inelastic scatteringDeep-inelastic scattering (DIS) and the observed scaling violations have been central to the formulation of Quantum Chromodynamics (QCD) as the gauge theory of the strong interactions [1,2]. Over the decades the available high precision experimental data from lepton-and neutrino scattering off fixed targets at CERN, FNAL and SLAC as well as from electronproton collisions at the HERA collider at DESY have successfully probed QCD in a wide kinematical range. The key observables are inclusive structure functions or differential cross sections which provide the theoretical description of the hard hadronic interactions in the QCD improved parton model. Precision predictions in perturbative QCD rest on the fact that we can separate the sensitivity to dynamics from different scales, i.e., the physics at scale of the nucleon mass from hard highenergy scattering at a large scale Q 2 . In Fig. 1 this is depicted for lepton-proton DIS in the one-boson exchange approximation, see e.g., Ref. [3] for the definitions of the kinematic variables.The factorization at a scale µ allows to express for instance the unpolarized inclusive structure functions

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“…m ps (κ S qc , κ S qc ) = 0. κ S qc has been determined in [10]. 3 The improvement term to the axial current, ∂ µ P together with improvement coefficient c A , [11] has been included. The mass improvement terms, together with their associated difference in improvement coefficients, b A , b P appear to be small and have been ignored here.…”

Section: The Lattice Approachmentioning

confidence: 99%

Determining the strange quark mass for 2-flavour QCD

Göckeler

Horsley

Irving

et al. 2006

Nuclear Physics B - Proceedings Supplements

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Using the O(a) Symanzik improved action an estimate is given for the strange quark mass for unquenched (n f = 2) QCD. The determination is via the axial Ward identity (AWI) and includes a non-perturbative evaluation of the renormalisation constant. Numerical results have been obtained at several lattice spacings, enabling the continuum limit to be taken. Our results indicate a value for the strange quark mass (in the MS-scheme at a scale of 2 GeV) in the range 100 -130 MeV. A comparison is also made with other recent lattice determinations of the strange quark mass using dynamical sea quarks.

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The four-loop β-function in quantum chromodynamics

Abstract: We present the analytical calculation of the four-loop QCD β-function within the minimal subtraction scheme.

Cited by 1,088 publications

References 20 publications

Renormalizable extra-dimensional models

Renormalizable extra-dimensional models

Status of perturbative QCD calculations for deep-inelastic scattering and related processes

Determining the strange quark mass for 2-flavour QCD

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