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I am looking for the Feynman rule of the 4-point gauge boson interaction of W+ W- -> Z Z. I am guessing it looks like the Yang Mills 4-point vertex for gluons, but with helicity included. Equation 8.81 in my professor's lecture notes seems to imply polarization, or am I misinterpreting? |
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It turns out that the vertex $X$ has to be contracted with the particle polarizations in the following manner, is $$X^{\mu \nu \alpha \beta} \epsilon_{1_\mu} \epsilon_{2_\nu} \epsilon_{3_\alpha} \epsilon_{4_\beta}$$ where $$X^{\mu \nu \alpha \beta} = 2 g^{\mu \nu} g^{\alpha \beta} - g^{\mu \alpha} g^{\nu \beta} - g^{\mu \beta} g^{\nu \alpha}$$ This results in: $$2(\epsilon_1 \cdot \epsilon_2) (\epsilon_3 \cdot \epsilon_4) - (\epsilon_1 \cdot \epsilon_3) (\epsilon_2 \cdot \epsilon_4) - (\epsilon_1 \cdot \epsilon_4) (\epsilon_2 \cdot \epsilon_3)$$ |
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