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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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have a look at – anna v Jan 21 '12 at 15:50
unfortunately the article does not give an expression for the vertex. I need that in order to calculate the amplitude. – Ben Ruijl Jan 21 '12 at 17:53
Always better to link to the abstract page both so that readers can read the abstract before deciding to download the paper and because that way they can look at the refers to and cited by links. – dmckee Jan 21 '12 at 18:49
this has a lagrangian and a table with couplings: . I found it by google, asking for "WW ZZ quartic coupling standard model" – anna v Jan 21 '12 at 19:54
It would be good to edit things like that into the question, so that we know that you've already tried the obvious techniques and why they're not working. – David Z Jan 22 '12 at 3:15
up vote 0 down vote accepted

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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