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

Abstract

We present Standard Model predictions for the complete set of phenomenologically relevant electroweak precision pseudo-observables related to the Z-boson: the leptonic and bottom-quark effective weak mixing anglessin2θℓeff, sin2θbeff, the Z-boson partial decay widths Γf, where f indicates any charged lepton, neutrino and quark flavor (except for the top quark), as well as the total Z decay width ΓZ, the branching ratios Rℓ, Rc, Rb, and the hadronic cross sectionσ0had. The input parameters are the masses MZ, MH and mt, and the couplings αs, α. The scheme dependence due to the choice of MW or its alternative Gμ as a last input parameter is also discussed. Recent substantial technical progress in the calculation of Minkowskian massive higher-order Feynman integrals allows the calculation of the complete electroweak two-loop radiative corrections to all the observables mentioned. QCD contributions are included appropriately. Results are provided in terms of simple and convenient parameterization formulae whose coefficients have been determined from the full numerical multi-loop calculation. The size of the missing electroweak three-loop or QCD higher-order corrections is estimated. We briefly comment on the prospects for their calculation. Finally, direct predictions for the Zf¯¯¯f vector and axial-vector form-factors are given, including a discussion of separate order-by-order contributions.