  We present a new way to interpret Top Standard Model measurements going
beyond the SMEFT framework. Instead of the usual paradigm in Top EFT, where the
main effects come from tails in momenta distributions, we propose an
interpretation in terms of new physics which only shows up at loop-level. The
effects of these new states, which can be lighter than required within the
SMEFT, appear as distinctive structures at high momenta, but may be suppressed
at the tails of distributions. As an illustration of this phenomena, we present
the explicit case of a UV model with a $\mathcal{Z}_2$ symmetry, including a
Dark Matter candidate and a top-partner. This simple UV model reproduces the
main features of this class of signatures, particularly a momentum-dependent
form factor with more structure than the SMEFT. As the new states can be
lighter than in SMEFT, we explore the interplay between the reinterpretation of
direct searches for colored states and Dark Matter, and Top measurements made
by ATLAS and CMS in the differential $t \bar t$ final state. We also compare
our method with what one would expect using the SMEFT reinterpretation, finding
that using the full loop information provides a better discriminating power.
