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

A 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, 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: $\frac{\sigma_{\text{L}}}{\sigma_{{\text{tot}}}} = 24.9 \pm4.5({\text{stat}}) \pm2.2({\text{syst}})\%$ at a mean energy of 198 GeV. The SDM elements are also used to determine the triple gauge couplings Δg1 Z,Δκγ,λγ and g4 Z, $\tilde{\kappa}_{Z}$ and $\tilde{\lambda}_{Z}$ . For the CP-violating couplings the results of single parameter fits are: $g_4^{{Z}} = -0.39^{+0.19}_{-0.20}$ $\tilde{\kappa}_{{Z}} = -0.09^{+0.08}_{-0.05}$ $\tilde{\lambda}_{{Z}} = -0.08\pm0.07 .$ The errors are a combination of statistical and systematic errors. All results are consistent with the Standard Model.