  We propose multiloop vacuum amplitudes as the optimal building blocks for
efficiently assembling theoretical predictions at high-energy colliders. This
hypothesis is strongly supported by the manifestly causal properties of the
loop-tree duality (LTD) representation of a vacuum amplitude. The vacuum
amplitude, acting as a kernel, encodes all the final states contributing to a
given scattering or decay process through residues in the on-shell energies of
the internal propagators. It also naturally implements gauge invariance and the
wave function renormalisation of the external legs. This methodological
approach, dubbed LTD causal unitary, leads to a novel representation of
differential cross sections and decay rates that is locally free of ultraviolet
and infrared singularities at all orders in perturbation theory. Unitary
threshold singularities also match between different phase-space residues. Most
notably, it allows us to conjecture for the first time the local functional
form of initial-state collinear singularities. The fulfillment of all these
properties provides a theoretical description of differential observables at
colliders that is well defined in the four physical dimensions of the
space-time.
