  We present the first proof-of-concept application to decay processes at
higher perturbative orders of LTD causal unitary, a novel methodology that
exploits the causal properties of vacuum amplitudes in the loop-tree duality
(LTD) and is directly well-defined in the four physical dimensions of the
space-time. The generation of loop- and tree-level contributions to the
differential decay rates from a kernel multiloop vacuum amplitude is shown in
detail, and explicit expressions are presented for selected processes that are
suitable for a lightweight understanding of the method. Specifically, we
provide a clear physical interpretation of the local cancellation of soft,
collinear and unitary threshold singularities, and of the local renormalisation
of ultraviolet singularities. The presentation is illustrated with numerical
results that showcase the advantages of the method.
