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

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In summary: Your name]In summary, to obtain the Feynman rule for the photon/W+/W- vertex in the Standard Model, you can use the Feynman diagram technique and the Feynman rules for propagators and vertices. By replacing partial derivatives with -i*p, you can eliminate the field terms in the Lagrangian and simplify the expression to get the correct result for the vertex rule.
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Muoniex
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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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Thank you for your question. The Feynman rule for the photon/W+/W- vertex can be derived using the Feynman diagram technique and the Feynman rules for propagators and vertices. Here is a step-by-step guide to obtaining the correct result:

1. Start by writing down the Feynman diagram for the photon/W+/W- vertex. It should have three external legs, corresponding to the photon (A), W+ (W1), and W- (W2).

2. Label the momenta of the external particles as p1, p2, and p3 for A, W1, and W2 respectively.

3. Write down the Feynman rules for the propagators and vertices involved in the diagram. For the photon, use the propagator D(p) = -igμν/p^2. For the W+ and W- particles, use the propagator D(p) = -i/((p^2 - m^2)). For the vertex, use the Feynman rule given in the homework equations.

4. Multiply the propagators and vertex together and simplify using the momentum conservation rule p1 + p2 + p3 = 0.

5. Use the trick mentioned in the forum post, where you replace the partial derivative with respect to the momentum p with -i*p. This will eliminate the fields terms in the Lagrangian.

6. Simplify the expression further by using the Feynman rules for the propagators and vertices. You should end up with the correct result for the Feynman rule of the photon/W+/W- vertex.

I hope this helps. If you have any further questions, please don't hesitate to ask. Good luck with your studies!
 

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

1. What is Feynman's rule for the Photon/W+/W- vertex?

Feynman's rule for the Photon/W+/W- vertex is a mathematical formula used in particle physics to calculate the probability of a photon interacting with a W+ or W- boson. It is based on the principles of quantum field theory and was developed by the physicist Richard Feynman in the 1940s.

2. How is Feynman's rule for the Photon/W+/W- vertex derived?

Feynman's rule for the Photon/W+/W- vertex is derived using Feynman diagrams, which are graphical representations of particle interactions. It involves calculating the amplitude of the process, which is then used to determine the probability of the interaction occurring.

3. What are the inputs and outputs of Feynman's rule for the Photon/W+/W- vertex?

The inputs of Feynman's rule for the Photon/W+/W- vertex are the momenta and polarization vectors of the particles involved in the interaction. The output is a numerical value representing the probability of the interaction occurring.

4. How is Feynman's rule for the Photon/W+/W- vertex used in experiments?

Feynman's rule for the Photon/W+/W- vertex is used in experiments to predict and analyze the outcomes of particle interactions. By calculating the probability of an interaction occurring, scientists can compare it to the actual results of the experiment and determine if it is consistent with the theory.

5. Are there any limitations to Feynman's rule for the Photon/W+/W- vertex?

Like any mathematical model, there are limitations to Feynman's rule for the Photon/W+/W- vertex. It is based on certain assumptions and may not accurately predict the outcomes of every particle interaction. Additionally, it does not take into account the effects of quantum gravity, which is still a topic of ongoing research.

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