Electroweak precision measurements of a nearly-degenerate Z^′-Z system

In this paper, we discuss the possibility to probe a nearly-degenerate Z^′-Z system by analyzing the Z-lineshape at an electron-positron collider. Compared with the usual Z^′ in the literature well separated with the standard model (SM) Z boson in mass, the nearly-degenerate Z^′-Z mixing affects the observed effective “oblique parameters” \(\widetilde{S}\) , \(\widetilde{T}\) , \(\widetilde{U}\) , and the effective deviation of “number of neutrino species” \(\delta {\widetilde{N}}_{\nu }\) in a more complicated way and cannot be simply computed perturbatively up to a particular order. Aiming at solving this problem, we write down a general simplified effective Lagrangian and enumerate some parameter spaces corresponding to some typical models, and suggest a method to extract the constraints by looking into the line-shape of the Z-like resonance at an electron-positron collider.