Correlations between polarisation states of W particles in the reaction e− e+ → W− W+ at LEP2 energies 189–209 GeV

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 (T T ), longitudinal–transverse plus transverse–longitudinal (LT ) and longitudinal–longitudinal (LL) have been determined using the final states WW→lνq¯q (l = e,μ). The two-particle joint polarisation probabilities, i.e. the spin density matrix elements ρT T , ρLT , ρLL, are measured as functions of the W− production angle, θW−, at an average reaction energy of 198.2 GeV. Averaged over all cos θW−, the following joint probabilities are obtained: ρ¯T T = (67±8)%, ρ¯LT = (30± 8)%, ρ¯LL = (3 ±7)%. These results are in agreement with the StandardModel predictions of 63.0%, 28.9% and 8.1%, respectively. The related polarisation cross-sections σT T , σLT and σLL are also presented.