Anomalous dimensions of gauge fields and gauge coupling beta-functions in the Standard Model at three loops

Abstract

We present the results for three-loop gauge field anomalous dimensions in the SM calculated in the background field gauge within the unbroken phase of the model. The results are valid for the general background field gauge parameterized by three independent parameters. Both quantum and background fields are considered. The former are used to find three-loop anomalous dimensions for the gauge-fixing parameters, and the latter allow one to obtain the three-loop SM gauge beta-functions. Independence of beta-functions of gauge-fixing parameters serves as a validity check of our final results.

23 pages, self-coupling normalization fixed, anc files corrected accordingly

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• Pole mass of the W boson at two-loop order in the pure MS-bar scheme
• Matching relations for decoupling in the Standard Model at two loops and beyond