Consistent Electroweak Phenomenology of a Nearly Degenerate $Z'$ Boson

Extracting constraints on kinetic mixing between a new $U(1)'$ gauge boson hiding under the Standard Model $Z$ boson resonance requires the formalism of non-Hermitian two-point correlation functions at 1-loop order. We derive self-consistent collider constraints on $Z'$ bosons with kinetic mixing in a narrow mass window around the $Z$ boson, considering both model-independent and model-dependent bounds. Our treatment elucidates the importance of both avoided level crossing and width suppression due to the quantum Zeno effect in interpreting the existing constraints. We also discuss the implications for future measurements on the $Z$-pole.