Theoretical underpinnings of CP-Violation at the High-energy Frontier

We present a general analysis for the discovery potential of CP-violation (CPV) searches in scattering processes at TeV-scale colliders in an effective field theory framework, using the SMEFT basis for higher dimensional operators. In particular, we systematically examine the CP-violating sector of the SMEFT framework in some well motivated limiting cases, based on flavour symmetries of the underlying heavy theory. We show that, under naturality arguments of the underlying new physics (NP) and in the absence of (or suppressed) flavour-changing interactions, there is only a single operator, $Q_{t\phi} = \phi^\dagger \phi \left(\bar q_3 t \right) \tilde{\phi} $ which alters the top-Yukawa coupling, that can generate a non-vanishing CP-violating effect from tree-level SM$\times$NP interference terms. We find, however, that CPV from $Q_{t\phi} = \phi^\dagger \phi \left(\bar q_3 t \right) \tilde{\phi} $ is expected to be at best of $O(1\%)$ and, therefore, very challenging if at all measurable at the LHC or other future high-energy colliders. We then conclude that a potentially measurable CP-violating effect of $O(10\%)$ can arise in high-energy scattering processes ONLY if flavour-changing interactions are present in the underlying NP; in this case a sizable CPV can be generated at the tree-level by pure NP$\times$NP effects and not from SM$\times$NP interference. We provide several examples of CPV at the LHC and at a future $e^+e^-$ collider to support these statements.