  We present the general expression of helicity amplitudes for generic
multi-body particle decays characterised by multiple decay chains. This is
achieved by addressing for the first time the issue of the matching of final
particle spin states among different decay chains in full generality for
generic multi-body decays, proposing a method able to match the exact
definition of spin states relative to the decaying particle ones. We stress the
importance of our result by showing that one of the matching method used in the
literature is incorrect, leading to amplitude models violating rotational
invariance. The results presented are therefore relevant for performing
numerous amplitude analysis, notably those searching for exotic structures like
pentaquarks.
