Space, time, and color in hadron production via $e^{+}{e}^{-}\to Z^0$ and $e^{+}{e}^{-}\to W^{+}{W}^{-}$

The time evolution of jets in hadronic $e^{+}{e}^{-}$ events at CERN LEP is investigated in both position and momentum space, with emphasis on effects due to color flow and particle correlations. We address dynamical aspects of the four simultaneously evolving, cross-talking parton cascades that appear in the reaction $e^{+}{e}^{-}\to \frac{{\gamma }^{*}}{Z^0}\to W^{+}{W}^{-}\to q_1{\overline{q}}_2{q}_3{\overline{q}}_4$, and compare with the familiar two-parton cascades in $e^{+}{e}^{-}\to Z^0\to q_1{\overline{q}}_2$. We use a QCD statistical transport approach, in which the multiparticle final state is treated as an evolving mixture of partons and hadrons, whose proportions are controlled by their local spacetime geography via standard perturbative QCD parton shower evolution and a phenomenological model for nonperturbative parton-cluster formation followed by cluster decays into hadrons. Our numerical simulations exhibit a characteristic "inside-outside" evolution simultaneously in position and momentum space. We compare three different model treatments of color flow, and find large effects due to cluster formation by the combination of partons from different $W$ parents. In particular, we find in our preferred model a shift of several hundred MeV in the apparent mass of the $W$, which is considerably larger than in previous model calculations. This suggests that the determination of the $W$ mass at LEP 2 may turn out to be a sensitive probe of spatial correlations and hadronization dynamics.