Factorization in processes of graviton scattering off electron for Z and W productions

The study of factorization in linearized gravity is extended to the graviton scattering processes with an electron for the massive vector boson productions such as $g e \rightarrow Z e$ and $g e \rightarrow W ν_e$. It is shown that every transition amplitude is completely factorized due to gravitational gauge invariance and Lorentz invariance. Also the explicit values of vector boson polarizations are obtained.

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