Atomic parity violation in cesium and implications for the 3 - 3 - 1 models

The parity violation in cesium atom is analysed in the framework of the models based on the SU(3)_C X SU(3)_L X U(1)_N gauge group. It is shown that in the minimal version, the main contribution to a deviation of weak charge \Delta Q_W due to direct Z' exchange is negative. New data on parity violation in the cesium atom seems not favour to the minimal version, while it gets a positive value in the version with right-handed neutrinos. We obtain a bound on the $Z'$ mass at a range from 1.4 TeV to 2.6 TeV. The allowed regions for the Z-Z'$mixing angle are also derived.