The analytical helicity amplitudes for Z -> 3 gamma, gamma gamma -> gamma Z and gamma Z -> gamma gamma via W-loop, charged scalar-loop

The analytic helicity amplitudes of Z -->, 3 gamma, gamma gamma --> Z gamma and gamma Z --> gamma gamma via W-loop and charged scalar-loop are presented. There is some difference between our results and those in Z. Phys. C60 (1993) 175 (E.W.N. Glover and A.G. Morgan) for Z --> 3 gamma via W-loop and fermion-loop, which has different physical meanings.