Standard model parameters in the tadpole-free pure MS¯ scheme

Abstract

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

Full two-loop QCD corrections to the Higgs mass in the MSSM with heavy superpartners

“…In the simplest heavy-SUSY setup in which the effective theory valid below the SUSY scale is just the SM, we can exploit the full two-loop calculations of the relation between m h , λ(Q EW ) and G F presented in refs. [85][86][87]. In section 3 we compared the results of two of those calculations, refs.…”

“…[89]. However, the full twoloop contributions to the relation between the pole Higgs mass, λ(Q EW ) and G F in the SM are also available [85][86][87]. These contributions can in principle be implemented in our EFT calculation, to prepare the ground for the eventual completion of the NNLL resummation of the large logarithmic corrections.…”

“…In recent years, after the LHC results pushed the expectations for the SUSY scale into the TeV range, the realization that an accurate prediction for the Higgs mass in the MSSM cannot prescind from the resummation of the large logarithmic corrections brought the EFT computation under renewed focus [63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78]. In the simplest scenario in which all of the SUSY particles as well as the heavy Higgs doublet of the MSSM are clustered around a single scale M S , so that the EFT valid below that scale is just the SM, the state of the art now includes: full one-loop and partial two-loop matching conditions for the quartic Higgs coupling at the SUSY scale, computed for arbitrary values of the relevant SUSY parameters [65,72]; full three-loop RGEs for all of the parameters of the SM Lagrangian [79][80][81][82][83][84]; full two-loop relations at the EW scale between the running SM parameters and a set of physical observables which include the pole Higgs mass [85][86][87]. The combination of these results allows for a full NLL resummation of the large logarithmic corrections to the Higgs mass, whereas the NNLL resummation can only be considered partial, because in refs.…”

Numerator seagull and extended Symmetries of Feynman Integrals

“…Earlier work on these diagrams includes [25][26][27][28][29][30] and references within [8] and [14]. The results of [8] were incorporated in a public computer code which relates the observable Standard Model parameters to Lagrangian parameters while accounting for some 2, 3 and even 4-loop contributions [31].…”

All two-loop scalar self-energies and tadpoles in general renormalisable field theories

“…In the Standard Model (SM), this is used to extract the Higgs quartic coupling λ, which, through a significant amount of work can now be done with high precision, where all of the relevant running parameters of the Lagrangian can now be extracted from calculations at full two-loop order [1,2] and partially at the three-and four-loop order [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. A code for calculating λ in Landau gauge, SMH [17], and codes for extracting all relevant SM parameters (the gauge couplings, top and bottom Yukawa couplings, and Higgs quartic coupling), mr [18,19] (which builds on the results of, inter alia, [20][21][22][23][24]) and SMDR [25], exist. As a result of this effort, the uncertainty on the measurement of the top mass is now more important than the scalar self-energies in the SM.…”