Electroweak two-loop corrections to the MW-MZ mass correlation in the Standard Model

TL;DR

This work delivers an exact fermionic two-loop computation of the radiative correction $\Delta r$ that relates the W and Z boson masses through muon decay, within the Standard Model. It details an on-shell renormalization framework and a careful separation of IR QED effects to yield IR-finite results, while also presenting the Higgs-mass dependence of the bosonic two-loop piece. The authors provide a precise numerical parametrisation for $M_W$ as a function of $M_H$ (up to 1 TeV) and compare it to prior top-quark-mass expansions, finding discrepancies at the level of a few MeV. They assess remaining theoretical uncertainties, estimate the impact of higher-order corrections, and discuss the implications for current and future collider tests of electroweak theory, with the complex-pole mass definition ensuring gauge-invariant renormalized quantities. Overall, the results strengthen precision tests of the SM and guide expectations for MW measurements at upcoming facilities.

Abstract

Recently exact results for the complete fermionic two-loop contributions to the prediction for the W-boson mass from muon decay in the electroweak Standard Model have been published [hep-ph/0007091]. This paper illustrates the techniques that have been applied for this calculation, in particular the renormalisation procedure and the treatment of IR-divergent QED contributions. Numerical results are presented in terms of simple parametrisation formulae and compared in detail with a previous result of an expansion up to next-to-leading order in the top-quark mass. An estimate of the remaining theoretical uncertainties of the MW-prediction from unknown higher-order corrections is given. For the bosonic two-loop corrections a partial result is presented, yielding the Higgs-mass dependence of these contributions.

Figures (13)

• Figure 1: Examples for types of fermionic two-loop diagrams contributing to muon decay.
• Figure 2: Two-loop vertex diagrams containing a triangle subgraph, which require a careful treatment of $\gamma_5$ in $D$ dimensions.
• Figure 3: Virtual (a) and real (b) QED corrections to muon decay in the Fermi Model.
• Figure 4: Examples for virtual IR-divergent diagrams contributing to muon decay in the Standard Model. Besides the one-loop diagram (a), at two-loop order, there are diagrams with four (b) and two (c) electromagnetic couplings.
• Figure 5: Examples for real bremsstrahlung diagrams in the two-loop calculation of muon decay in the Standard Model, involving one-loop diagrams (a) and two-loop diagrams with four (b) and two (c) QED couplings.