The 4-loop quark mass anomalous dimension and the invariant quark mass

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

doi:10.1016/s0370-2693(97)00660-6

Cited by 570 publications

(521 citation statements)

References 19 publications

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“…Remarkably, the two determinations have been derived using different approaches. The APE result (19) has been obtained within HQET, while the determination (20), by Collins et al, is obtained from the NRQCD study of the B-meson spectrum in the static limit. The last error in eqs.…”

Section: The B-quark Massmentioning

confidence: 99%

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Quark masses on the lattice: light and heavy

Lubicz

2001

Nuclear Physics B - Proceedings Supplements

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I review the current status of lattice calculations of light and heavy quark masses. Significant progresses, in these studies, have been allowed by the introduction of improved actions and non-perturbative renormalization techniques. Current determinations of light quark masses are accurate at the level of 20%, where the main source of uncertainty is represented by the quenching error. The determination of the bottom quark mass is accurate at the impressive level of 2%. As final averages of lattice results, I quote m ud (2 GeV) = (4.5 ± 1.0) MeV, ms(2 GeV) = (110 ± 25) MeV and m b (m b ) = (4.26 ± 0.09) GeV.

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Section: The B-quark Massmentioning

confidence: 99%

“…The last error in eqs. (19) and (20) represents the residual uncertainty due to the neglecting of higher orders in the perturbative expansion of δm. For comparison, this uncertainty was estimated to be of the order of 200 MeV at NLO [50] and 100 MeV at N 2 LO [45] respectively.…”

Section: The B-quark Massmentioning

confidence: 99%

Quark masses on the lattice: light and heavy

Lubicz

2001

Nuclear Physics B - Proceedings Supplements

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“…One issue which might arise with this is the appearance of Casimirs other than products of (2.8). From the nature of the Feynman diagrams, it is easy to convince oneself that new Casimirs, such as those which appeared at four loops in the MS β-function and quark mass anomalous dimensions in QCD, [8,9], will not occur at three loops in the NATM.…”

Section: Preliminariesmentioning

confidence: 99%

“…Given this intriguing connection between the NATM and QCD it is important to understand the quantum and renormalization properties of the former theory in more detail. For instance, in QCD the four loop β-function and mass anomalous dimensions have recently been determined in MS in [8,9]. These built on the earlier loop calculations of [10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Three-loop renormalization of the SU(N) non-abelian Thirring model

Bennett

Gracey

1999

Nuclear Physics B

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Abstract. We renormalize to three loops a version of the Thirring model where the fermion fields not only lie in the fundamental representation of a non-abelian colour group SU (N c ) but also depend on the number of flavours, N f . The model is not multiplicatively renormalizable in dimensional regularization due to the generation of evanescent operators which emerge at each loop order. Their effect in the construction of the true wave function, mass and coupling constant renormalization constants is handled by considering the projection technique to a new order. Having constructed the MS renormalization group functions we consider other massless independent renormalization schemes to ensure that the renormalization is consistent with the equivalence of the non-abelian Thirring model with other models with a four-fermi interaction. One feature to emerge from the computation is the establishment of the fact that the SU (N f ) Gross Neveu model is not multiplicatively renormalizable in dimensional regularization. An evanescent operator arises first at three loops and we determine its associated renormalization constant explicitly.

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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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The 4-loop quark mass anomalous dimension and the invariant quark mass

Cited by 570 publications

References 19 publications

Quark masses on the lattice: light and heavy

Quark masses on the lattice: light and heavy

Three-loop renormalization of the SU(N) non-abelian Thirring model

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

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