Abstract

Measurements of the trilinear gauge boson vertex coupling (TGC) parameters and the W polarisation of W $^{+}$ W $^{-}$ boson pairs produced in e $^{+}$ e $^{-}$ collisions are presented. The data were recorded by the OPAL experiment at LEP during 1998, where a total integrated luminosity of 183 pb $^{-1}$ was obtained at a centre-of-mass energy of 189 GeV. Only events where one W boson decays into a quark and an anti-quark, and the other W decays into a lepton and a neutrino are used. The selected data sample comprises of 1075 events.

All the measurements are performed through a spin density matrix analysis of the W boson decay products. In addition to this, an analysis of the W production angle is performed to further constrain the measured trilinear gauge boson coupling parameters.

The sets of TGC parameters measured are $\Delta\kappa_{\gamma}$ - $\lambda$ - $\Delta g^{z}_{1}$ and $\tilde{\kappa}_{z}$ - $\tilde{\lambda}_{z}$ - $g^{z}_{4}$ . The first set are all CP-conserving, where as the second set are all CP-violating. Both sets of parameters may have anomalous values without violating the ${\rm SU}(2)_{L}\times {\rm U}(1)_{Y}$ gauge symmetry of the electroweak Lagrangian. The measured values of the CP-conserving parameters are:

$\displaystyle \mbox{$\Delta\kappa_{\gamma}$}$	$\displaystyle =$	$\displaystyle -0.235^{+0.282}_{-0.232}$
$\displaystyle \mbox{$\lambda$}$	$\displaystyle =$	$\displaystyle -0.082^{+0.102}_{-0.095}$
$\displaystyle \mbox{$\Delta g^{z}_{1}$}$	$\displaystyle =$	$\displaystyle -0.038^{+0.102}_{-0.095}$

$\displaystyle \mbox{$\tilde{\kappa}_{z}$}$	$\displaystyle =$	$\displaystyle -0.184^{+0.091}_{-0.065}$
$\displaystyle \mbox{$\tilde{\lambda}_{z}$}$	$\displaystyle =$	$\displaystyle -0.136^{+0.161}_{-0.194}$
$\displaystyle \mbox{$g^{z}_{4}$}$	$\displaystyle =$	$\displaystyle +0.070^{+0.263}_{-0.255}$

In addition to the measurement of the TGC parameters, the SDM analysis is used to directly measure the W bosons polarisation states. The W boson may have either longitudinal or transverse polarisation. The fraction of W bosons produced with longitudinal polarisation is found to be $\sigma_{\rm L}/\sigma_{\rm total} = (21.9 \pm 3.4 \pm 1.6)\%$ , where the first error is statistical and the second systematic.

The joint W-pair production fractions were found to be; $\sigma_{\rm TT}/\sigma_{\rm total} = (76.8 \pm 9.0 \pm 3.2) \%$ , $\sigma_{\rm LL}/\sigma_{\rm total} = (20.6 \pm 7.2 \pm 1.8) \%$ and $\sigma_{\rm TL}/\sigma_{\rm total} = (2.6 \pm 14.7 \pm 3.8) \%$ .