Electroweak Feynman Rules: Confusion about the photon-W boson interaction term

  • #1
Elmo
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TL;DR Summary
A confusion about the photon-W boson interaction term
This screenshot is from Quantum Field Theory by Mandl and Shaw, 2nd Edition.

I had a question about the vertex factor feynman rule (given below the daigram) of the photon and W+, W- interaction term. Its lagrangian density is given in the third and fourth line of (19.3 a)

What confuses me is the fact that this diagram shows all the momenta directed inwards. Is it the only possible way this coupling can exist or can we also show something like say, the W+ and W- boson momenta directed outwards from the vertex and photon coming inwards ? How will the vertex factor change in that case ? Is it simply a matter of flipping the signs of the momenta in the vertex factor expression ?

Also, is it possible to have a vertex where there is something like a Bremsstrahlung on a single W+ or W- line ?
Screenshot (469).png
 
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  • #2
The directions are arbitrary labels. It's like voltages or currents in electric circuits. What direction you use to define them is arbitrary, choosing the opposite direction just flips the sign of all values.

W -> W+photon is possible, sure. Here is a diagram.
 
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  • #3
Sorry for the late reply.
I just require a bit more clarification on the answer. When @mfb says to flip the signs of all values for oppositely directed momenta, does it mean to flip the signs of momenta only or also of the iota and e ?

Also how will the vertex factor get modified for W->W+photon ?
And how will it be different for W+ and W- ?
I have included a picture of what I think the vertex factors ought to look like, based upon my reference Mandl and Shaw. Do please have a look at it.
 

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1. What are Electroweak Feynman Rules?

Electroweak Feynman Rules are a set of mathematical rules used in quantum field theory to calculate the probability of particle interactions involving the electromagnetic and weak nuclear forces. These rules are based on Feynman diagrams, which represent the possible paths of particles during an interaction.

2. Why is there confusion about the photon-W boson interaction term?

There is confusion about the photon-W boson interaction term because the standard Electroweak Feynman Rules do not include a direct interaction between these two particles. This is because the photon is massless and the W boson is massive, making it difficult to reconcile their interactions within the framework of the Electroweak Theory.

3. How is the photon-W boson interaction term usually handled?

The photon-W boson interaction term is usually handled using a mathematical technique called "gauge fixing." This involves modifying the Electroweak Feynman Rules to include a virtual particle, called a "ghost," which cancels out the unwanted interaction between the photon and W boson. This allows for consistent calculations while still preserving the principles of the Electroweak Theory.

4. Is there evidence for the existence of the photon-W boson interaction term?

There is currently no experimental evidence for the existence of the photon-W boson interaction term. However, the predictions of the Electroweak Theory, including the gauge fixing technique, have been extensively tested and confirmed through experiments at particle accelerators such as the Large Hadron Collider.

5. How does understanding Electroweak Feynman Rules contribute to our understanding of the universe?

Understanding Electroweak Feynman Rules is crucial for understanding the fundamental forces and particles that make up our universe. The Electroweak Theory, which is based on these rules, has been incredibly successful in predicting and explaining the behavior of particles at the subatomic level. It also provides insight into the early stages of the universe and the processes that govern its evolution.

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