Electroweak Effective Charges and their relation to Physical Cross Sections

Abstract

In quantum electrodynamics with fermions f = e,μ..., knowledge of the vacuum polarization spectral function determined from the tree level e^+e^- -> f^+f^- cross sections, together with a single low energy measurement of the fine structure constant α, enables the construction of the one-loop effective charge α_eff(q^2) for all q^2. It is shown how an identical procedure can be followed in the electroweak sector of the Standard Model to construct three gauge-, scale- and scheme-independent one-loop electroweak effective charges and an effective weak mixing angle from the tree level e^+e^- -> W^+W^-, ZH and e^+ν_e -> W^+Z, W^+γ, W^+H differential cross sections, together with three low energy measurements, which may be chosen to be αand the masses of the W and Z bosons. It is found that the corresponding proper self-energy-like functions thus constructed are identical to those obtained in the pinch technique framework. In this way, it is shown how the concept of effective charges in the electroweak Standard Model is as well-defined and unique as in quantum electrodynamics.