I provide a calculation at full two-loop order of the complex pole squared mass of the $W$ boson in the Standard Model in the pure $\overline{\text{MS}}$ renormalization scheme, with Goldstone boson mass effects resummed. This approach is an alternative to earlier ones that use on-shell or hybrid renormalization schemes. The renormalization scale dependence of the real and imaginary parts of the resulting pole mass is studied. Both deviate by about $\pm 4\mathrm{MeV}$ from their median values as the renormalization scale is varied from 50 to 200 GeV, but the theory error is likely larger. A surprising feature of this scheme is that the two-loop QCD correction has a larger scale dependence, but a smaller magnitude, than the two-loop non-QCD correction, unless the renormalization scale is chosen very far from the top-quark mass.

• Received 29 March 2015

DOI:https://doi.org/10.1103/PhysRevD.91.114003