generated and the event is hadronized directly. We set $p^{\rm{min}}_T=1{\,\mathrm{GeV}}$ throughout this work;

3.  If $p_T \geq p^{\rm{min}}_T$, the momenta of the $W$ boson, bottom quark and gluon are calculated using the generated values of the radiative variables. Doing so, yields two possible values of $E_W$ that must both be retained and used in the remainder of the calculation. If the resulting momenta do not lie within the physically allowed region of phase space, we veto this configuration, set $p^{\rm{max}}_T = p_T$ and return to step 1;

4.  Events within the physical phase space are accepted with a probability given by the ratio of the true to overestimated integrands in Eqs. \[eq:POSudakov2\] and \[eq:SudakovOver\] respectively. If the event is rejected, we set $p^{\rm{max}}_T = p_T$ and return to step 1;

Using this procedure, a trial emission is generated for each dipole, $\mathcal{D}_i$, in Eq. \[eq:POSudakov2\]. The configuration which gives the highest $p_T$ emission is selected. The existing  framework, detailed in [@Hamilton:2008pd], is then used to generate the remainder of the parton shower.

Parton Level Results {#sec:TopQuarkRes}
--------------------

To validate our implementation of the algorithm described in Sec. \[sec:TopQuarkImp\], Dalitz style plots were generated for the decay $t \rightarrow W b$ 