A study of $e^{+}e^{-} \to W^{+}W^{-}$ at centre-of-mass energies between 161 and 209 GeV

The LEP accelerator ran above the threshold for the production of W boson pairs for five years, at a range of centre-of-mass energies between 161 and 209 GeV. The data collected by the DELPHI experiment in this period has been used to study some properties of the W boson. The selection of e sup + e sup - -> W sup + /W sup - events from the data was performed with a discriminant technique. The properties of a variety of such techniques were investigated; a significant improvement over the commonly used linear discriminants was obtained by using a quadratic discriminant, and by applying transformations to the input observables. The selected events were used to measure the W boson branching ratios, and the evolution of the total and differential cross-sections with energy. The branching ratios are sensitive to the W couplings to the fermions, and the cross-sections are sensitive to the coupling both to fermions and to the other electro-weak gauge bosons, the photon and the Z sup 0. The measurement of the W branching ratios observed no deviations from the expected relative coupling strengths between the W boson and the fermions. The results were combined to give a measurement of the hadronic branching ratio: BR sub q 68.78 +- 0.56(stat.) +- 0.63(syst.)%, in good agreement with the standard model. This measurement was used to extract the value of the CKM matrix element vertical bar V sub c sub s vertical bar 1.036 +- 0.028(stat.) +- 0.031(syst.). Measurements of the total and differential e sup + e sup - -> W sup + W sup - cross-sections were in good agreement with the predictions of the standard model, thus confirming the gauge structure of the model.