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

The deviation $\de Q_{\mathrm{W}}$ 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 $Z'$ 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 $\de Q_\mathrm{W}$ 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 $Z'$ boson, the $Z-Z'$ and $W-Y$ mixing angles with the more appropriate values: $M_{Z'} > 564\ \mathrm{GeV}, -0.018<\sin \va < 0$ and $|\sin \theta| < 0.043$.