Complete Two Loop Bosonic Contributions to the Muon Lifetime in the Standard Model

TL;DR

The last missing correction to the muon lifetime in the standard model at O(alpha(2)) coming from gauge and Higgs boson loops is presented and a shift of the W boson mass is presented.

Abstract

The last missing correction to the muon lifetime in the Standard Model at O(alpha^2) coming from gauge and Higgs boson loops is presented. The associated contribution to the parameter Delta r in the on-shell scheme ranges from 6 times 10^{-5} to -4 times 10^{-5} for Higgs boson masses from 100 GeV to 1 TeV. This result translates into a shift of the W boson mass which does not exceed +/- 1 MeV in the same range and amounts in particular to approximately -0.8 MeV for a 115 GeV Higgs boson.

Figures (3)

• Figure 1: A typical muon decay diagram a) and the contributions to its large mass expansion according to the momenta b) $k_1$-soft, $k_2$-soft; c) soft-hard; d) hard-soft; e) hard-hard.
• Figure 2: $\Delta r$ as function of the Higgs boson mass (solid line) and the leading term in the large Higgs mass expansion (dashed line).
• Figure 3: $W$ boson mass shift generated by two loop bosonic corrections.