Z boson pole mass at two-loop order in the pure MS-bar scheme

TL;DR

This paper calculates the Z boson pole mass at two-loop order in the Standard Model using the MS-bar scheme, providing a precise theoretical prediction that aligns with experimental uncertainties.

Contribution

It presents the first full two-loop calculation of the Z boson mass in the pure MS-bar scheme, including resummation of Goldstone boson effects.

Findings

Scale dependence comparable to experimental uncertainty

Theoretical error likely larger than scale variation

Provides a precise theoretical framework for Z boson mass prediction

Abstract

I obtain the complex pole squared mass of the Z boson at full two-loop order in the Standard Model in the pure MS-bar renormalization scheme. The input parameters are the running gauge couplings, the top-quark Yukawa coupling, the Higgs self-coupling, and the vacuum expectation value that minimizes the Landau gauge effective potential. The effects of non-zero Goldstone boson mass are resummed. Within a reasonable range of renormalization scale choices, the scale dependence of the computed pole mass is found to be comparable to the current experimental uncertainty, but the true theoretical error is likely somewhat larger.