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arXiv · 1703.08532

Four-loop QCD propagators and vertices with one vanishing external momentum

B. Ruijl·T. Ueda·J. A. M. Vermaseren·A. Vogt
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Abstract

We have computed the self-energies and a set of three-particle vertex functions for massless QCD at the four-loop level in the MSbar renormalization scheme. The vertex functions are evaluated at points where one of the momenta vanishes. Analytical results are obtained for a generic gauge group and with the full gauge dependence, which was made possible by extensive use of the Forcer program for massless four-loop propagator integrals. The bare results in dimensional regularization are provided in terms of master integrals and rational coefficients; the latter are exact in any space-time dimension. Our results can be used for further precision investigations of the perturbative behaviour of the theory in schemes other than MSbar. As an example, we derive the five-loop beta function in a relatively common alternative, the minimal momentum subtraction (MiniMOM) scheme.

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B. Ruijl, T. Ueda, J. A. M. Vermaseren, A. Vogt. 2017-05-01. Four-loop QCD propagators and vertices with one vanishing external momentum. https://doi.org/10.1007/jhep06(2017)040

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