| Shrnutí: | A determination of the single W spin density matrix (SDM) elements in the reaction e+e-→W+W-→lνqq (l=e/μ) is reported at centre-of-mass energies between 189 and 209∈GeV. The data sample used corresponds to an integrated luminosity of 520∈pb-1 taken by DELPHI between 1998 and 2000. The single W SDM elements, ρττ'W± (τ,τ'= ± 1 or 0), are determined as a function of the W- production angle with respect to the e- beam direction and are obtained from measurements of the W decay products by the application of suitable projection operators, Λττ', which assume the V-A coupling of the W-boson to fermions. The measured SDM elements are used to obtain the fraction of longitudinally polarised Ws, with the result: σ {L}{σ} = 24.9 pm4.5( pm2.2({)\% at a mean energy of 198∈GeV. The SDM elements are also used to determine the triple gauge couplings Δg1Z,Δκγ,λγ and g4Z, ̃κ_Z and ̃λ {Z} . For the CP-violating couplings the results of single parameter fits are: g4Z = -0.39+0.19-0.20 ̃κZ = -0.09+0.08-0.05 ̃λZ = -0.08±0.07 The errors are a combination of statistical and systematic errors. All results are consistent with the Standard Model. © 2008 Springer-Verlag / Società Italiana di Fisica.
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