Analytical helicity amplitudes for Z -> 3 gamma and it's related processesand discussion of polarization vectors

The analytical helicity amplitudes for Z-->3 gamma and it's related process es via w-loop and charged scalar loop are presented. There are some differe nces between our results and those in Glover paper for Z-->3 gamma via w-lo op and fermion loop. Although these differences do not contradict the resul t of total decay width for Z-->3 gamma, but the different helicity amplitud es have measurable physical meanings. We discuss the definition of polariza tion vector and point out the error of Glover paper.