Three-loop QCD corrections to the electroweak boson masses

TL;DR

This paper calculates three-loop QCD corrections to the masses of the Higgs, W, and Z bosons in the Standard Model, improving theoretical precision and reducing scale dependence.

Contribution

It provides the first three-loop QCD corrections to electroweak boson masses as functions of MSbar parameters, using a tadpole-free scheme, and includes results in the SMDR code.

Findings

Mass dependences on renormalization scale are smaller than experimental uncertainties.

Higgs mass correction is state-of-the-art.

W and Z mass results agree with existing schemes.

Abstract

I find the three-loop corrections at leading order in QCD to the physical masses of the Higgs, W, and Z bosons in the Standard Model. The results are obtained as functions of the $\overline{\rm{MS}}$ Lagrangian parameters only, using the tadpole-free scheme for the vacuum expectation value. The dependences of the computed masses on the renormalization scale are found to be smaller than present experimental uncertainties in each case. In the case of the Higgs boson mass, the new result is the state-of-the-art, while the results for $W$ and $Z$ are in good numerical agreement with corresponding results in the on-shell and hybrid schemes. These results are now included in the SMDR (Standard Model in Dimensional Regularization) computer code.