Atomic parity violation in the economical 3-3-1 model

The deviation $\text{de}{Q}_{\mathrm{W}}$ of the weak charge from its standard model prediction due to the mixing of the $W$ boson with the charged bilepton $Y$ as well as of the $Z$ boson with the neutral $Z^{\mathrm{\prime }}$ and the real part of the non-Hermitian neutral bilepton $X$ in the economical 3-3-1 model is established. Additional contributions to the usual $\text{de}{Q}_{\mathrm{W}}$ expression in the extra $\mathrm{U}(1)$ models and the left-right models are obtained. Our calculations are quite different from previous analyzes in this kind of the 3-3-1 models and give the limit on mass of the $Z^{\mathrm{\prime }}$ boson, the $Z-Z^{\mathrm{\prime }}$ and $W-Y$ mixing angles with the more appropriate values: $M_{Z’} > 564
$\mathrm{G}\mathrm{e}\mathrm{V}$, -0.018<\sin \va < 0$and$|\sin \theta| < 0.043$.