Complete electroweak two-loop corrections to Z boson production and decay

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, ${\Gamma }_Z$, partial decay widths ${\Gamma }_{e,\mu },{\Gamma }_{\tau },{\Gamma }_{\nu },{\Gamma }_u,{\Gamma }_c,{\Gamma }_{d,s},{\Gamma }_b$, branching ratios $R_l,R_c,R_b$ and the hadronic peak cross-section, ${\sigma }_{\mathrm{had}}^0$. Theoretical intrinsic uncertainties from missing higher orders are also discussed.