Electroweak Precision Measurements of a Nearly-Degenerate $Z^\prime$-$Z$ System

TL;DR

This paper explores how nearly-degenerate $Z'$ and $Z$ bosons influence collider measurements, proposing a method to analyze their mixing effects on the $Z$-lineshape to constrain new physics models.

Contribution

It introduces a simplified effective Lagrangian and a novel approach to extract constraints from the $Z$-lineshape in nearly-degenerate $Z'$-$Z$ systems, addressing complexities beyond perturbative calculations.

Findings

Proposes a method to analyze $Z$-lineshape for nearly-degenerate $Z'$-$Z$ systems.

Provides parameter space mappings for typical models.

Highlights the impact on oblique parameters and neutrino count deviations.

Abstract

In this paper, we discuss the possibility to probe a nearly-degenerate $Z^{\prime}$-$Z$ system by analyzing the $Z$-lineshape at an electron-positron collider. Compared with the usual $Z^{\prime}$ in the literature well separated with the standard model (SM) $Z$ boson in mass, the nearly-degenerate $Z^{\prime}$-$Z$ mixing affects the observed effective ``oblique parameters'' $\tilde{S}$, $\tilde{T}$, $\tilde{U}$, and the effective deviation of ``number of neutrino species'' $\delta \tilde{N}_{\nu}$ 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.