Standard Model parameters in the tadpole-free pure $\overline{\mathrm{MS}}$ scheme

Abstract

We present an implementation and numerical study of the Standard Model couplings, masses, and vacuum expectation value (VEV), using the pure $\overline{\mathrm{MS}}$ renormalization scheme based on dimensional regularization. Here, the $\overline{\mathrm{MS}}$ Lagrangian parameters are treated as the fundamental inputs, and the VEV is defined as the minimum of the Landau gauge effective potential, so that tadpole diagrams vanish, resulting in improved convergence of perturbation theory. State-of-the-art calculations relating the $\overline{\mathrm{MS}}$ inputs to on-shell observables are implemented in a consistent way within a public computer code library, SMDR (Standard Model in Dimensional Regularization), which can be run interactively or called by other programs. Included here for the first time are the full 2-loop contributions to the Fermi constant within this scheme and studies of the minimization condition for the VEV at 3-loop order with 4-loop QCD effects. We also implement, and study the scale dependence of, all known multi-loop contributions to the physical masses of the Higgs boson, the W and Z bosons, and the top quark, the fine structure constant and weak mixing angle, and the renormalization group equations and threshold matching relations for the gauge couplings, fermion masses, and Yukawa couplings.

26 pages. The latest SMDR code can be obtained from https://davidgrobertson.github.io/SMDR/ Typo in eq. (4.3) fixed; does not affect code or numerical results. SMDR v1.3 now includes 3-loop contributions to the Higgs, W, and Z masses, and to GFermi

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