and are shown in Fig. \[fig:top\_Dalitz\]. The Dalitz variables, $x_W$ and $x_g$, were defined by the relation, $x_i = \frac{2E_i}{m_t}$, where $E_i$ is the energy of particle $i$ in the rest frame of the top quark. The left-hand plot in Fig. \[fig:top\_Dalitz\] shows the distribution obtained using the POWHEG style correction. In this case, $x_g$ is the energy fraction of the gluon generated using the full real-emission matrix element. The distribution on the right-hand side of Fig. \[fig:top\_Dalitz\] was generated using the conventional parton shower, limited to one emission in the final state, and so here $x_g$ is the energy fraction of a gluon produced using the parton shower splitting kernels. On both distributions, the black outline indicates the physical phase space boundaries. The enclosed area is divided into a section populated by radiation from the bottom quark (above the green dashed line), sections populated by radiation from the top quark (below the blue dotted lines) and a *dead region* (between the blue dotted and green dashed lines) that corresponds to hard gluon radiation and is not populated by the conventional parton shower. These boundaries correspond to the theoretical limits of the  parton shower with symmetric phase space partitioning, described 