# Constraining heavy neutral gauge boson $Z'$ in the 3 - 3 - 1 models by weak charge data of Cesium and proton

## TL;DR

This paper uses weak charge measurements of Cesium and proton to set bounds on the $Z'$ boson in 3-3-1 models, favoring certain parameter choices and suggesting a unique treatment for the third quark family.

## Contribution

It provides new constraints on the $Z'$ mass and model parameters in 3-3-1 gauge theories based on recent weak charge data, highlighting the significance of gauge boson mixing.

## Key findings

- Lower bound on $Z'$ mass is 1.27 TeV.
- Models with $eta = ext{0,} \, eta = ext{±}1/\sqrt{3}$ are favored.
- Models with $eta=\pm \sqrt{3}$ are ruled out.

## Abstract

The recent experimental data of the weak charges of Cesium and proton is analyzed in the framework of the models based on the $\mbox{SU}(3)_C\times \mbox{SU}(3)_L \times \mbox{U}(1)_X$ (3-3-1) gauge group, including the 3-3-1 model with CKS mechanism (3-3-1CKS) and the general 3-3-1 models with arbitrary $\beta$ (3-3-1$\beta$) with three Higgs triplets. We will show that at the TeV scale, the mixing among neutral gauge bosons plays significant effect. Within the present values of the weak charges of Cesium and proton we get the lowest mass bound of the extra heavy neutral gauge boson to be 1.27 TeV. The results derived from the weak charge data, perturbative limit of Yukawa coupling of the top quark, and the relevant Landau poles favor the models with $\beta =\pm 1/\sqrt{3}$ and $\beta = 0$ while ruling out the ones with $\beta= \pm \sqrt{3}$. In addition, there are some hints showing that in the 3-3-1 models, the third quark family should be treated differently from the first twos.