• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • Thread starter Muoniex
  • Start date
  • #1
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 Feynmann 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 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:
  • Like
Likes Raymont

Answers and Replies

Related Threads on Feynman's rule for Photon/W+/W- vertex

Replies
1
Views
2K
Replies
2
Views
507
Replies
1
Views
862
Replies
2
Views
2K
  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
3
Views
9K
  • Last Post
Replies
22
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
Top