Renormalization constants and beta functions for the gauge couplings of the Standard Model to three-loop order

Abstract

We compute the beta functions for the three gauge couplings of the Standard Model in the minimal subtraction scheme to three loops. We take into account contributions from all sectors of the Standard Model. The calculation is performed using both Lorenz gauge in the unbroken phase of the Standard Model and background field gauge in the spontaneously broken phase. Furthermore, we describe in detail the treatment of ${\gamma }_5$ and present the automated setup which we use for the calculation of the Feynman diagrams. It starts with the generation of the Feynman rules and leads to the bare result for the Green's function of a given process.

44 pages, 9 figures; v2: sign in eq.(29) corrected; final result unchanged

References in corpus (3)

• FeynRules - Feynman rules made easy
• Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model
• Minimal Supersymmetric SU(5) and Gauge Coupling Unification at Three Loops

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