Anomalous neutral gauge boson interactions and simplified models

Trilinear $Z$ boson interactions are sensitive probes both of new sources of $CP$ violation in physics Beyond the Standard Model and of new particle thresholds. Measurements of trilinear $Z$ interactions are typically interpreted in the frameworks of anomalous couplings and effective field theory, both of which require care in interpretation. To obtain a quantitative picture of the power of these measurements when interpreted in a TeV-scale context, we investigate the anatomy of $ZZZ$ interactions and consider two minimal and perturbative simplified models which induce such interactions through new scalar and fermion loops at the weak scale, focusing on $ZZ$ and vector boson fusion-induced $Zjj$ production at the LHC and $ZZ$ production at a future $e^+ e^-$ collider. We show that both threshold and non-threshold effects often are small compared to the sensitivity of the LHC, while the increased sensitivity of a future lepton collider should allow us to constrain such scenarios through associated electroweak precision effects complementary to direct searches at hadron colliders.