to describe the singular behaviour resulting from emissions from the decay products. The dipole used to describe radiation from the top quark is as follows \_i = |\_B|\^2. \[eq:initialDipole\] It contains only soft enhancements since, in the top quark rest frame, collinear enhancements are suppressed.

Using the above information, the hardest emission in the shower can then be generated according to Eq. \[eq:POSudakov2\] using the veto algorithm[^3], which proceeds as follows:

1.  Trial values of the radiative phase space variables are generated. The transverse momentum of the emission is generated by solving \^[[over]{}]{}(p\_T ) = (- \^[p\^[[max]{}]{}\_T]{}\_[p\_T]{} p\_T( \_R) ) = , \[eq:SudakovOver\] where $p^{\rm{max}}_T = \frac{\left(m_t -m_W \right)^2 -m_b^2} {2 \left(m_t - m_W \right)}$ is the maximum possible $p_T$ of the gluon. $y_{\rm{max}}$ and $y_{\rm{min}}$ are the upper and lower bounds on the gluon rapidity, chosen to overestimate the true rapidity range. $C$ is a constant chosen such that the integrand in Eq. \[eq:SudakovOver\] always exceeds the integrand in Eq. \[eq:POSudakov2\] and $\mathcal{R}$ is a random number distributed uniformly in the range $[0,1]$. Values of $y$ and $\phi$ are generated uniformly in the ranges $[y_{\rm{min}}, y_{\rm{max}}]$ and $[0, 2 \pi]$ respectively;

2.  If $p_T < p^{\rm{min}}_T$, no radiation is 