Modified interactions in the top-quark electroweak sector: exploiting unitarity violating effects at the amplitude level to probe New Physics

We present a broad study of collider processes that embed $2 \to 2$ scattering amplitudes involving top quarks in the Electroweak sector. We parametrise the modified interactions using the Standard Model Effective Field Theory framework and discuss how the New Physics effects lead to unitarity violating behaviour at the amplitude level. For each scattering amplitude we compute the helicity amplitudes in the high energy limit paying special attention to the effects of the higher dimensional operators. We also discuss whether and to what extent the unitarity violating effects are retained in physical processes at colliders.