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

## TL;DR

This paper develops a comprehensive computational framework for Standard Model parameters using the pure ar{MS} scheme, improving precision and convergence in theoretical predictions through advanced multi-loop calculations and a public code library.

## Contribution

It introduces the SMDR code for consistent ar{MS} scheme calculations, including full 2-loop Fermi constant and 3-loop VEV minimization, enhancing precision in Standard Model parameter determination.

## Key findings

- Full 2-loop contributions to Fermi constant implemented.
- Studies of VEV minimization at 3-loop order with 4-loop QCD effects.
- Scale dependence analyzed for physical masses and couplings.

## Abstract

We present an implementation and numerical study of the Standard Model couplings, masses, and vacuum expectation value (VEV), using the pure $\overline{\rm{MS}}$ renormalization scheme based on dimensional regularization. Here, the $\overline{\rm{MS}}$ 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 $\overline{\rm{MS}}$ 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.