On Colour Rearrangement in Hadronic W$^+$W$^-$ Events

We discuss the possibility of colour rearrangement in $\ee \to \W^+ \W^- \to \q_1 \qbar_2 \q_3 \qbar_4$ events, i.e.\ that the original colour singlets $\q_1 \qbar_2$ and $\q_3 \qbar_4$ may be transmuted, for instance, into new singlets $\q_1 \qbar_4$ and $\q_3 \qbar_2$. The effects on event properties could be quite large if such a rearrangement would occur instantaneously, so that gluon emission would be restricted to each of the new singlets separately. We argue that such a scenario is unlikely for two reasons. Firstly, the $\W^+$ and $\W^-$ usually decay at separate times after the $\W^+\W^-$ production, which leads to large relative phases for energetic radiation off the two constituents of a rearranged system, and a corresponding dampening of the QCD cascades. Secondly, within the perturbative scenario the colour transmutation appears only in order $\alpha_s^2$ and is colour-suppressed. Colour reconnection at longer time scales is quite feasible, however, and may affect the fragmentation phase. If so, the nature of non-perturbative QCD can be probed in a new way. We formulate several alternative toy models and use these to estimate the colour reconnection probability as a function of the event kinematics. Possible consequences for LEP~2 events are illustrated, with special attention to systematic errors in $\W$ mass determinations.