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

In summary, the discussion revolves around the complexities and misunderstandings related to the interaction term between photons and W bosons in the electroweak theory. It highlights the nuances of the Feynman rules that govern these interactions, addressing common points of confusion and clarifying the mathematical formulations used in particle physics. The aim is to provide a clearer understanding of how these fundamental particles interact within the framework of electroweak unification.
  • #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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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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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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FAQ: Electroweak Feynman Rules: Confusion about the photon-W boson interaction term

What is the photon-W boson interaction term in electroweak theory?

The photon-W boson interaction term describes how the photon interacts with the W bosons (W+, W-, and W0) in the framework of electroweak theory. This interaction is crucial for processes involving charged currents, where W bosons mediate the weak force, and it includes terms in the Lagrangian that account for the coupling between the electromagnetic field and the weak isospin fields.

Why is there confusion about this interaction term?

Confusion often arises due to the complexity of the electroweak theory, particularly the mixing of the electromagnetic and weak interactions. The mathematical formalism involves gauge bosons and their interactions, which can be non-intuitive. Additionally, the presence of both charged and neutral W bosons and their interactions with photons can lead to misunderstandings about how these particles behave and interact with one another.

How do Feynman rules apply to the photon-W boson interaction?

Feynman rules provide a systematic way to translate the terms in the Lagrangian of a quantum field theory into graphical representations (Feynman diagrams) and mathematical expressions for calculating scattering amplitudes. For the photon-W boson interaction, the rules specify how to draw the interaction vertices, assign momenta, and calculate contributions to processes such as electron-neutrino scattering or W boson production in high-energy collisions.

What are the implications of the photon-W boson interaction in particle physics?

The photon-W boson interaction has significant implications in particle physics, particularly in processes that involve the weak force. It plays a key role in the unification of electromagnetic and weak interactions and is essential for understanding phenomena such as neutrino interactions, the decay of W bosons, and the production of charged leptons in high-energy collisions. This interaction is also vital for the predictions made by the Standard Model of particle physics.

How can one resolve the confusion surrounding the photon-W boson interaction?

To resolve confusion, it is helpful to study the underlying principles of electroweak theory, including gauge symmetry and the role of spontaneous symmetry breaking. Familiarizing oneself with the mathematical framework of quantum field theory, particularly the derivation of Feynman rules, can also aid in understanding. Additionally, consulting comprehensive resources, attending lectures, and engaging in discussions with experts in the field can clarify misconceptions and deepen comprehension of the photon-W boson interaction.

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