that figure respectively. On the other hand, one can fix a Born-like configuration ${{\bf 1}}$ and, using the inverse of the maps ${{\cal P}_{{{\mathbb H}}\to{{\mathbb S}}}^{(\pm)}}$ (which we denote by ${{\cal P}_{{{\mathbb S}}\to{{\mathbb H}}}^{(\pm)}}$), work out the real-emission configurations to be used in the computation of the integrand of $I_{{{\mathbb S}}}^{(\pm)}$: [[**2**]{}]{}\^+=[[P]{}\_[[[S]{}]{}]{}\^[(+)]{}]{}[[**1**]{}]{}, [[**2**]{}]{}\^-=[[P]{}\_[[[S]{}]{}]{}\^[(-)]{}]{}[[**1**]{}]{}. \[invmap\] As we have already stressed, although there is an ample freedom in choosing ${{\cal P}_{{{\mathbb H}}\to{{\mathbb S}}}^{(\pm)}}$, it is best to adopt a form motivated by what the PSMC does when branching. In practice, it is therefore convenient first to obtain ${{\cal P}_{{{\mathbb S}}\to{{\mathbb H}}}^{(\pm)}}$ from the PSMC, and then (by inverting them) ${{\cal P}_{{{\mathbb H}}\to{{\mathbb S}}}^{(\pm)}}$. In the case of , ${{\cal P}_{{{\mathbb S}}\to{{\mathbb H}}}^{(\pm)}}$ amount to performing a boost of the Born-level four momenta in the transverse direction, to balance the transverse momentum of the parton produced in the branching ($c(k_2)$ in eq. (\[Rproc\])), followed by a boost in the longitudinal direction, to e.g. the lab frame. The information on the latter is equivalent to the assignments of the momentum fractions of the incoming particles. The prescription for the transverse boost given above is obviously trivial in the case of $V$ production (since $k_{1{{\scriptscriptstyle}T}}=-k_{2{{\scriptscriptstyle}T}}$), 