simulation of the hardest emission in the shower and hence generate the Born configuration using only $B \left(\Phi_N \right)$, the leading order contribution in Eq. \[eq:Bbar\]. As such, we use the existing LO  implementation of top quark decay and modify the shower such that the hardest emission is generated according to Eq. \[eq:POSudakov2\]. Justification for excluding the normalisation factor of the POWHEG correction will be given in Sect. \[sec:BSMDecays\].

Application of the POWHEG correction to top quark decays, along with top quark pair production in $e^+ e^-$ collisions, has been previously studied in [@LatundeDada:2008bv] for massless bottom quarks. In this work, we retain the mass of the bottom quark throughout.

Implementation in   {#sec:TopQuarkImp}
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In , the decays of fundamental particles are performed in the rest frame of the decaying particle. In this frame, we are free to choose the orientation of the $W$ boson to be along the negative $z$-direction and so, at LO, the bottom quark is orientated along positive $z$-direction. The squared, spin and colour averaged matrix element for the LO process is given by |\_B|\^2 = (m\_t\^4+m\_b\^4-2m\_w\^4+m\_t\^2m\_w\^2+m\_b\^2m\_w\^2-2m\_t\^2m\_b\^2 ), where $m_t$, $m_b$ and $m_W$ are the masses of the top quark, bottom quark and $W$ boson respectively 