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 $W^{\pm }\to {\ell }^{\pm }\nu$ (angles relative to the $e^{-}$ beam direction): $d\sigma /d\cos {\theta }_{+}d\cos {\theta }_{-}\sim (1-\cos {\theta }_{+})(1+\cos {\theta }_{-})(1+\cos {\theta }_{-}\cos {\theta }_{+})$ . If only the ${\ell }^{-}$ is observed, its angular distribution is $d\sigma /d\cos {\theta }_{-}\sim (1+\cos {\theta }_{-})(3-\cos {\theta }_{-})$, 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 $\nu$-exchange, is contrasted with that due to $\gamma$- and $Z$-exchange, which is relevant for annihilation in the helicity state $e_R^{-}{e}_L^{+}$.

Comments: 10 pages, 6 figures, LaTeX, simpler derivation of main results, also added a comparison with Monte Carlo expectations