Study of W-boson polarisations and triple gauge boson couplings in the reaction e + e - →W + W - at LEP 2

determination of the single W spin density matrix (SDM) elements in the reaction e + e - →W + W - →lνqq̄(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, ρ ττ’ 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, Λ ττ’ , 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_tot = 24.9 ±4.5(stat) ±2.2(syst)% at a mean energy of 198 GeV. The SDM elements are also used to determine the triple gauge couplings Δg 1 Z ,Δκ γ ,λ γ and g 4 Z , κ̃_Z and λ̃_Z . For the CP-violating couplings the results of single parameter fits are: g_4^Z = -0.39^+0.19_-0.20 κ̃_Z = -0.09^+0.08_-0.05 λ̃_Z = -0.08±0.07 . The errors are a combination of statistical and systematic errors. All results are consistent with the Standard Model.