Searching for new physics effects in future $W$ mass and $\sin^2\theta_W (Q^2)$ determinations

TL;DR

This paper explores how a hypothetical dark Z boson could influence electroweak measurements, potentially explaining recent anomalies in W mass and weak mixing angle data, and discusses its testability at future colliders.

Contribution

It analyzes the effects of a dark Z boson with kinetic and mass mixing on electroweak observables, providing new insights into possible explanations for recent experimental anomalies.

Findings

Dark Z boson can account for the CDF W mass anomaly within 2σ.

The model predicts deviations in the weak mixing angle at low energies.

Future colliders can test the existence of such dark Z bosons.

Abstract

We investigate the phenomenology of the dark $Z$ boson, $Z_d$, which is associated with a new Abelian gauge symmetry and couples to the standard model particles via kinetic mixing $\varepsilon$ and mass mixing $\varepsilon_Z^{}$. We examine two cases: (i) $Z_d$ is lighter than the $Z$ boson, and (ii) $Z_d$ is heavier than that. In the first case, it is known that $Z_d$ causes a deviation in the weak mixing angle at low energies from the standard model prediction. We study the prediction in the model and compare it with the latest experimental data. In the second case, the $Z$-$Z_d$ mixing enhances the $W$ boson mass. We investigate the effect of $Z_d$ on various electroweak observables including the $W$ boson mass using the $S$, $T$, and $U$ parameters. We point out an interesting feature: in the limit $\varepsilon \to 0$, the equation $S = - U$ holds independently of the mass of $Z_d$ and the size of $\varepsilon_Z^{}$, while $|S|\gg |U|$ in many new physics models. We find that the dark $Z$ boson with a mass of $O(100)~\mathrm{GeV}$ with a relatively large mass mixing can reproduce the CDF result within $2\sigma$ while avoiding all other experimental constraints. Such dark $Z$ bosons are expected to be tested at future high-energy colliders.