Feynman Diagrams: Exploring Electroweak Vertices

• Jodahr
In summary: V†du |u>Thus the amplitude for the conjugate process above, W+ + d → u, is<0|ubar W+ |du> = <0|bar(u| V†du |u>) = <0|bar(u| V*ud |u>) = <0|u Vud |u>so we see that the second vertex must also be proportional to Vud, but conjugated.So why is one vertex left-handed and the other right-handed? Well, if you think about it, to form a W+ boson, you need a left-handed and a right-handed component. So what the first vertex does is to form a left-handed W+ from a left-handed u and
Jodahr
I have a question about Feynman Diagrams:

let's say we have a process: up antidown -> W+ -> up antidown...

the first vertex is like V_CKM G PL ( mixing, gamma, projector)
the second is the same..only with the complex conjugate CKM matrix...
but why?...

If I compute the M* I have to bar the vertices..and there I got the same vertex..with the same flow..but there I would change PL to PR and interchange PL and Gamma..why is that the case?

Jodahr said:
I have a question about Feynman Diagrams:

let's say we have a process: up antidown -> W+ -> up antidown...

the first vertex is like V_CKM G PL ( mixing, gamma, projector)
the second is the same..only with the complex conjugate CKM matrix...
but why?...

If I compute the M* I have to bar the vertices..and there I got the same vertex..with the same flow..but there I would change PL to PR and interchange PL and Gamma..why is that the case?

Hello, in my opinion the answer is the following: the Feynman diagram you are considering is composed of two vertices: in the first an up is destroyed, an antidown is destroyed and a W+ is created; in the second vertex an up is created, an antidown is created and a W+ is destroyed; so, roughly speaking, the first is associated with a term in the lagrangian like (u dbar W-), while the second with (ubar d W+), that is its hermitian conjugate (of course I have forgot all the contraction matrices...); this is the origin of the conjugation of the CKM matrix paramters (and, of course, one should be careful with the imaginary units!)

Francesco

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I think another way of looking at it is like this.

That Feynman diagram also describes the processes

u → W+ + d
W+ + d → u​

as all I have done here is replace the incoming anti-d with an outgoing d, and the outgoing anti-d with an incoming d.

The CKM matrix, as defined, is the factor for 'converting' down-type quarks to up-type, eg

|u> = Vud |d>​

Provided only the three known generations of quarks exist, the CKM matrix must be unitary, and hence

V-1 = V

so

|d> = V*ud |u>​

Last edited:

What are Feynman diagrams?

Feynman diagrams are graphical representations of particle interactions in quantum field theory. They were developed by physicist Richard Feynman in the 1940s as a visual tool for calculating the probabilities of different particle interactions.

What do Feynman diagrams show?

Feynman diagrams show the possible interactions between particles, including the exchange of virtual particles. They also represent the conservation of energy and momentum in these interactions.

Why are Feynman diagrams important?

Feynman diagrams are important because they provide a visual representation of complex quantum field theory calculations. They allow scientists to predict the outcomes of particle interactions and make accurate predictions about the behavior of subatomic particles.

How do Feynman diagrams relate to electroweak vertices?

Feynman diagrams are used to explore the interactions between particles, including the electroweak force. The vertices in a Feynman diagram represent where particles interact and exchange energy, and can be used to study the electroweak force between particles.

What are some applications of Feynman diagrams?

Feynman diagrams have many applications in particle physics, including in the study of the Standard Model and in the development of theories for new particles and interactions. They are also used in experiments to test and confirm the predictions of quantum field theory.

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