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

Abstract

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 Al, Ab, 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, Z, partial decay widths e,μ, τ, ν, u, c, d,s, b, branching ratios Rl, Rc, Rband the hadronic peak cross-section, σ0had. Theoretical intrinsic uncertainties from missing higher orders are also discussed.