Complete fermionic two-loop results for the M_W-M_Z interdependence

Abstract

The complete fermionic two-loop contributions to the prediction for the W-boson mass from muon decay in the electroweak Standard Model are evaluated exactly, i.e. no expansion in the top-quark and the Higgs-boson mass is made. The result for the W-boson mass is compared with the previous result of an expansion up to next-to-leading order in the top-quark mass. The predictions are found to agree with each other within about 5 MeV. A simple parameterization of the new result is presented, approximating the full result better than 0.4 MeV for M_H < 1 TeV.

Figures (4)

• 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: Different contributions to $\Delta r$ as a function of $M\mathrm{H}$H$$M_$\mathrm{H}$$$. The one-loop contribution, $\Delta r^{(\alpha)}$, is supplemented by the two-loop and three-loop QCD corrections, $\Delta r^{(\alpha)}_{\mathrm{QCD}} \equiv \Delta r^{(\alpha\alpha_{\mathrm s})} + \Delta r^{(\alpha\alpha_{\mathrm s}^2)}$, and the fermionic electroweak two-loop contributions, $\Delta r^{(\alpha^2)} \equiv \Delta r^{(N_{\mathrm{f}} \alpha^2)} + \Delta r^{(N_{\mathrm{f}}^2 \alpha^2)}$. For comparison, the effect of the two-loop corrections induced by a resummation of $\Delta\alpha$, $\Delta r^{(\alpha^2)}_{\Delta\alpha}$, is shown separately.
• Figure 4: The SM prediction for $M\mathrm{W}$W$$M_$\mathrm{W}$$$ as a function of $M\mathrm{H}$H$$M_$\mathrm{H}$$$ for $m\mathrm{t}$t$$m_$\mathrm{t}$$= 174.3 \pm 5.1$ GeV is compared with the current experimental value, $M\mathrm{W}$W$$M_$\mathrm{W}$$^{\mathrm{exp}} = 80.419 \pm 0.038$ GeV mori00, and the experimental 95% C.L. lower bound on the Higgs-boson mass, $M\mathrm{H}$H$$M_$\mathrm{H}$$= 107.9$ GeV mhlimit.