Angular Distribution of Decay Leptons from e^+e^- \to W^+W^- at Threshold

Abstract

The reaction $ e^+e^- \to W^+W^-$ produces a $W$-boson pair with a non-trivial spin correlation at threshold. This correlation leads to a characteristic angular correlation between the leptons produced in $W^{\pm} \to \ell ^{\pm} ν$ (angles relative to the $e^-$ beam direction): $d σ/d \cos θ_+ d \cos θ_- \sim (1-\cos θ_+) (1+ \cos θ_-) (1+\cos θ_- \cos θ_+) $ . If only the $\ell^-$ is observed, its angular distribution is $d σ/ d \cos θ_- \sim (1+\cos θ_-)(3-\cos θ_-) $, implying a forward-backward asymmetry of 3/8. An analytic result is also given for the azimuthal correlation. These results are reproduced by a Monte Carlo program, that also enables us to study the effects of the $W$ decay width. The threshold behaviour, which stems from the dominance of $ν$-exchange, is contrasted with that due to $γ$- and $Z$-exchange, which is relevant for annihilation in the helicity state $e^-_Re^+_L$.