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, 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.

Electroweak pseudo-observables and Z-boson form factors at two-loop accuracy

“…In this study, we have presented some phenomenologically useful applications of the recently completed electroweak two-loop calculation of Z-boson vertex corrections [36,37]. The work collects multi-year efforts of several groups for predictions of the EWPOs related to the Z peak up to electroweak full two-loop accuracy, supplemented by leading QCD higher-order terms.…”

“…Results for the partial and total Z widths, branching ratios and σ 0 had including the full two-loop corrections have first been published in Ref. [37]. They can be expressed in simple parameterization formulae, which are adequate for most phenomenological applications.…”

“…• Complete one-loop corrections [23], which have been re-computed for this work, and full two-loop [33,35,37] electroweak corrections;…”

“…We reproduced by an independent calculation the contribution of the bosonic electroweak two-loop corrections using the methods of Ref. [37]. The corrections can be expressed in terms of a weak form factor ∆κ (α 2 ,bos) , where…”

“…After several papers on approximate/partial higher-order corrections, the complete two-loop weak corrections were determined in a series of papers from 2004 to 2018 [27][28][29][30][31][32][33][34][35][36][37]. The correct formulation of the interplay of the 2→2 loop corrections with higher order real QED corrections in the S-matrix approach, also called un-folding of the effective 2→2 Born terms from the realistic 2→n observables, is a topic on its own.…”