  The theory of particle scattering is concerned with transition amplitudes
between states that belong to unitary representations of the Poincar\'e group.
The latter acts as the isometry group of Minkowski spacetime $\mathbb{M}$,
making natural the introduction of relativistic tensor fields encoding the
particles of interest. Since the Poincar\'e group also acts as a group of
conformal isometries of null infinity $\mathcal{I}$, massless particles can
also be very naturally encoded into Carrollian conformal fields living on
$\mathcal{I}$. In this work we classify the two- and three-point correlation
functions such Carrollian conformal fields can have in any consistent quantum
theory of massless particles and arbitrary dimension. We then show that bulk
correlators of massless fields in $\mathbb{M}$ explicitly reduce to these
Carrollian conformal correlators when evaluated on $\mathcal{I}$, although in
the case of time-ordered bulk correlators this procedure appears singular at
first sight. However we show that the Carrollian correlators of the descendant
fields are perfectly regular and precisely carry the information about the
corresponding S-matrix elements.
