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 $A_l,A_b$, 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, ${\Gamma }_{\mathrm{Z}}$, 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.

Comments: 10 pages