Correlations between polarisation states of

In a study of the reaction e − e +→W − W + with the DELPHI detector, the probabilities of the two W particles occurring in the joint polarisation states transverse–transverse (TT), longitudinal–transverse plus transverse–longitudinal (LT) and longitudinal–longitudinal (LL) have been determined using the final states $WW{\rightarrow}l\nu q\bar{q}$ (l=e,μ). The two-particle joint polarisation probabilities, i.e. the spin density matrix elements ρ TT , ρ LT , ρ LL , are measured as functions of the W − production angle, $\theta _{W^{-}}$, at an average reaction energy of 198.2 GeV. Averaged over all $\cos\theta_{W^{-}}$, the following joint probabilities are obtained: $$\bar{\rho}_{TT}=(67\pm8)\%,$$ $$\bar{\rho}_{LT}=(30\pm8)\%,$$ $$\bar{\rho}_{LL}=(3\pm7)\%.$$ These results are in agreement with the Standard Model predictions of 63.0%, 28.9% and 8.1%, respectively. The related polarisation cross-sections σ TT , σ LT and σ LL are also presented