Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement

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This article presents results for the last unknown two-loop contributions to the Z-boson partial widths and Z-peak cross-section. These are the so-called bosonic electroweak two-loop corrections, where "bosonic" refers to diagrams without closed fermion loops. Together with the corresponding results for the Z-pole asymmetries A l , A b , which have been presented earlier, this completes the theoretical description of Z-boson precision observables at full two-loop precision within the Standard Model. The calculation has been achieved through a combination of different methods: (a) numerical integration of Mellin-Barnes representations with contour rotations and contour shifts to improve convergence; (b) sector decomposition with numerical integration over Feynman parameters; (c) dispersion relations for sub-loop insertions. Numerical results are presented in the form of simple parameterization formulae for the total width, Γ Z , partial decay widths Γ e,µ , Γ τ , Γ ν , Γ u , Γ c , Γ d,s , Γ b , branching ratios R l , R c , R b and the hadronic peak cross-section, σ 0 had . Theoretical intrinsic uncertainties from missing higher orders are also discussed.