Crafting polarisations for top, $W$ and $Z$

We put forward a method to tune the polarisation state of decaying heavy particles (top quarks and $W\mathrm{/}Z$ bosons) in a pre-existing Monte Carlo sample. With this technique, dubbed as `custom angle replacement’, the decay angular distributions are modified in such a way that the desired polarisation state is reproduced, while all the production kinematics are unchanged. A non-trivial test of this approach is presented for the top quark semileptonic decay $t\to Wb\to \mathrm{\ell }\nu b$, with $\mathrm{\ell }=e,\mu$, in which the decay distribution is four-dimensional and involves three different Lorentz frames. The proposed method is ideally suited to obtain event samples with polarised heavy particles, as required by experimental measurements of polarisation and spin correlations.