  Modified interactions in the electroweak sector may lead to scattering
amplitudes that grow with energy compared to their Standard Model (SM)
counterparts. We present a detailed study of all $2\to2$ scattering amplitudes
involving at least one top quark and a pair of EW bosons. We analyse the high
energy behaviour of the amplitudes using the Standard Model Effective Field
Theory (SMEFT) to parametrise the departures from the SM. We discuss the origin
of the energy growth that arise from effective contact interactions by
appealing to the Goldstone equivalence theorem and find that the amplitudes
obey expected patterns of (non-)interference. The results are connected to
unitary-violating behaviour in the framework of anomalous SM interactions.
Therein, we identify the appearance of additional growth due to the violation
of $SU(2)$ gauge symmetry that leads to substantial differences between the
SMEFT and the anomalous couplings approaches. We also discuss the embeddings of
the scattering amplitudes into physical collider processes, presenting the
parametric SMEFT sensitivity to relevant top quark operators and paying special
attention to the extent to which the high energy behaviour of the $2\to2$
amplitude is retained in the actual processes accessible at colliders. The
effective $W$ approximation is exploited to gain analytical insight into the
embeddings of the $2\to2$ helicity amplitudes. Finally, we provide a compendium
of processes detailing numerous directions in which the SMEFT parameter space
can be accessed through high energy top quark processes in current and future
colliders.
