The decay of the Z-boson into three photons via W-boson loops

The fourth rank polarization tensors of {gamma}-{gamma} scattering via {ital W}-boson loops in the standard model by using a nonlinear {ital R}{sub {xi}} gauge, and via charged scalar meson loops in some nonstandard models, are calculated in terms of three transcendental functions of {ital B}({ital x}), {ital T}({ital x}), and {ital I}({ital x},{ital y}). Expressions for the helicity amplitudes are also presented. The total cross section of {gamma}-{gamma} scattering via {ital W}-boson loops in the low energy approximation agrees with what was gained by using a linear {ital R}{sub {xi}} gauge. Also a summary of our calculation of {ital Z}{r_arrow}{gamma}{gamma}{gamma} via {ital W}-boson loops in the nonlinear {ital R}{sub {xi}} gauge is given, which agrees with the results of Glover and Morgan.