Consistent electroweak phenomenology of a nearly degenerate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>Z</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math> boson

Extracting constraints on the kinetic mixing of a new <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:msup><a:mo stretchy="false">)</a:mo><a:mo>′</a:mo></a:msup></a:math> gauge boson hiding under the Standard Model <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>Z</e:mi></e:math> boson resonance requires the formalism of non-Hermitian two-point correlation functions at 1-loop order. We derive self-consistent collider constraints on <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>Z</g:mi><g:mo>′</g:mo></g:msup></g:math> bosons with kinetic mixing in a narrow mass window around the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>Z</i:mi></i:math> boson, considering both model-independent and model-dependent bounds. Our treatment elucidates the importance of both avoided level crossing and the dispersive seesaw effect in interpreting the existing constraints. We also discuss the implications for future measurements on the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>Z</k:mi></k:math>-pole.