Standard Model parameters in the tadpole-free pure $\overline{\rm{MS}}$ scheme
Stephen P. Martin, David G. Robertson
备注：
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
本文构建公开代码库 SMDR，在无蝌蚪图的纯 $\overline{\rm{MS}}$ 方案中一致实现标准模型参数的多圈转换、匹配与重整化群演化，并纳入 Fermi 常数完整 2 圈及 VEV 高阶研究。
摘要：
我们提出了对标准模型耦合、质量和真空期望值（VEV）的一种实现与数值研究，采用基于维数正规化的纯 $\overline{\rm{MS}}$ 重整化方案。在此，$\overline{\rm{MS}}$ 拉格朗日参数被视为基本输入，而 VEV 被定义为 Landau 规范有效势的极小值，从而使蝌蚪图消失，带来微扰论收敛性的改善。将 $\overline{\rm{MS}}$ 输入与在壳观测量联系起来的最新计算，以一致的方式在公开计算机代码库 SMDR（Standard Model in Dimensional Regularization，维数正规化中的标准模型）中实现；该代码库既可交互式运行，也可由其他程序调用。本文首次纳入该方案中 Fermi 常数的完整 2 圈贡献，并研究 3 圈阶且含 4 圈 QCD 效应的 VEV 极小化条件。我们还实现并研究了 Higgs 玻色子、W 与 Z 玻色子及顶夸克物理质量、精细结构常数和弱混合角的所有已知多圈贡献，以及规范耦合、费米子质量和 Yukawa 耦合的重整化群方程与阈值匹配关系的标度依赖性。
英文摘要：
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.
Institute for Theoretical Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院理论物理研究所）；Institute for Particle Physics Phenomenology, Durham University（达勒姆大学粒子物理现象学研究所）
The heavy quark-antiquark asymmetry in the variable flavor number scheme
Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心）；Johannes Kepler University（约翰内斯·开普勒大学）；Research Institute for Symbolic Computation (RISC)（符号计算研究所）；CERN（欧洲核子研究中心）
