We analyze the potential of CLIC based on e- gamma collisions to search for new $Z$ gauge boson. Single Z production at e-gamma colliders in two SU(3)_C X SU(3)_L X U(1)_N models: the minimal model and the model with right-handed (RH) neutrinos is studied in detail. Results show that new Z gauge bosons can be observed at the CLIC, and the cross sections in the model with RH neutrinos are bigger than those in the minimal one.
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