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Three-loop Three-Linear Vertices and Four-Loop MOM beta functions in massless QCD

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arxiv hep-ph/0007088 v1 pith:2I4C2IVW submitted 2000-07-10 hep-ph

K.G. Chetyrkin (U. of Freiburg , U. of Karlsruhe) , A. Retey (U. of Karlsruhe) This is my paper · ORCID
classification hep-ph
keywords four-loopfunctionsmomentumthree-loopbeta-functioncorrespondingmasslessmsbar
verification ladder T0 review T1 audit T2 compute T3 formal

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In this paper we present a full set of 2- and 3-point functions for massless QCD at three-loop order in the MSbar scheme. The vertex functions are evaluated at the asymmetric point with one vanishing momentum. These results are used to relate the MSbar coupling constant to that of various momentum subtraction renormalization schemes at three-loop order. With the help of the known four-loop MS-bar beta-function we then determine the four-loop coefficients of the corresponding MOM beta-functions. As an application we consider the momentum dependence (running) of the three-gluon asymmetrical vertex recently computed within the lattice approach by Ph. Boucaud et al. (JHEP 04 006 (2000)). An account of the four-loop term in the corresponding beta-function leads to a significant (around 30%) decrease of the value of the non-perturbative power-suppressed correction to the running.

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Cited by 3 Pith papers

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  1. Four loop Green's functions involving the $n$ $=$ $2$ moment of the Wilson operator

    hep-ph 2024-11 conditional novelty 6.0 of 10

    Four-loop MSbar expressions are computed for all single-scale quark two-point Green's functions with a second-moment twist-2 Wilson operator insertion, including operator mixing and operator correlation functions.

  2. Gluon mass scale through the Schwinger mechanism

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    A comprehensive review showing how massless composite poles in QCD vertices can generate the gluon mass scale, with a BSE-based computation reaching m=367 MeV against the 354 MeV lattice value.

  3. Renormalisation

    hep-ph 2025-11 unverdicted novelty 1.0 of 10

    An introductory review of renormalisation procedures, the renormalisation group, and scale-setting optimisation in gauge theories such as QCD.

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