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Third-order mixed electroweak-QCD corrections to the W-boson mass prediction from the muon lifetime

Ievgen Dubovyk, Ayres Freitas, Janusz Gluza, Johann Usovitsch

Abstract

We present the calculation of the so far missing ${\cal O}(α^2α_\mathrm{s})$ corrections to the quantity $Δr$, which relates the Fermi constant to the W-boson mass, and enables precision predictions of the latter. While the ${\cal O}(α^2α_\mathrm{s})$ corrections from diagrams with two closed fermion loops are already known, we here focus on the subset with one closed fermion loop, which is a substantially more complex problem. The calculation has been carried out through a combination of analytical and numerical techniques for the three-loop integrals and the on-shell renormalization. The impact of the new corrections is numerically significant, raising the Standard Model prediction for the W-boson mass by more than 3 MeV.

Third-order mixed electroweak-QCD corrections to the W-boson mass prediction from the muon lifetime

Abstract

We present the calculation of the so far missing corrections to the quantity , which relates the Fermi constant to the W-boson mass, and enables precision predictions of the latter. While the corrections from diagrams with two closed fermion loops are already known, we here focus on the subset with one closed fermion loop, which is a substantially more complex problem. The calculation has been carried out through a combination of analytical and numerical techniques for the three-loop integrals and the on-shell renormalization. The impact of the new corrections is numerically significant, raising the Standard Model prediction for the W-boson mass by more than 3 MeV.
Paper Structure (6 sections, 32 equations, 1 figure, 2 tables)

This paper contains 6 sections, 32 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Description of the calculation
  3. Renormalization
  4. Treatment of $\gamma_5$
  5. Matching with Fermi theory
  6. Numerical results and conclusion

Figures (1)

  • Figure 1: Sample diagrams for ${\cal O}(\alpha^2\alpha_\mathrm{s})$ corrections to muon decay in the full SM (a--g), and for the matching to the Fermi model (h,i). The symbols $\times$ and $\otimes$ denote ${\cal O}(\alpha_\mathrm{s})$ and ${\cal O}(\alpha\alpha_\mathrm{s})$ counterterms, respectively, whereas the black squares represent effective four-fermion interactions in the Fermi model.