# Feynman's rule for Photon/W+/W- vertex

## 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:
$$\partial_\mu \rightarrow -i k_\mu$$

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:

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

With
$$W_{\mu\nu}=\partial_\mu W_\nu -\partial _\nu W_\mu$$
$$F_{\mu\nu}=\partial_\mu A_\nu -\partial _\nu A_\mu$$

And the Feynmann rule for a $$W^+_\mu (p_1) W_\nu (p_2) A_\rho (p_3)$$ vertex is supposed to be:
$$-ie[g_{\mu\nu}(p_2-p_1)_\rho+g_{\nu\rho}(p_3-p_2)_\mu+g_{\mu\rho}(p_1-p_3)_\nu]$$

## The Attempt at a Solution

Edit: I have realised 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.

Last edited:
• Raymont