- #1

Muoniex

- 5

- 1

## Homework Statement

Hello there!

I've been trying to obtain the Feynman rule (tree level) for a photon/W+/W- vertex in SM, but I don't really know hoy to get it.

I've been told that there's a trick to obtain these rules, which consists in changing partials for momentums:

[tex]\partial_\mu \rightarrow -i k_\mu[/tex]

And then eliminating the fields terms in the Lagrangian and multiplicatying them for i, but i don't get to the correct result...

## Homework Equations

The gamma/W/W+ interaction is given by:

[tex]\mathcal{L}=ie(W^{\mu\nu}W_\mu^+A_\nu-W^+_{\mu\nu}W^\mu A^\nu-W^+_\mu W_\nu F^{\mu\nu})[/tex]

With

[tex]W_{\mu\nu}=\partial_\mu W_\nu -\partial _\nu W_\mu[/tex]

[tex]F_{\mu\nu}=\partial_\mu A_\nu -\partial _\nu A_\mu[/tex]

And the Feynman rule for a [tex]W^+_\mu (p_1) W_\nu (p_2) A_\rho (p_3)[/tex] vertex is supposed to be:

[tex]-ie[g_{\mu\nu}(p_2-p_1)_\rho+g_{\nu\rho}(p_3-p_2)_\mu+g_{\mu\rho}(p_1-p_3)_\nu][/tex]

## The Attempt at a Solution

Edit: I have realized my solution was wrong, but I still can't get to the right answer. Do you know where can I find a deduction of that vertex's rule, or another vertex's rule deduction to use it as a guide?

Thanks.

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