Anomaly cancellation triangle

In summary, the conversation discusses the contributions of fermions in a triangle diagram for Z \rightarrow W^-W^+, and whether or not they all contribute equally to the constraint of \sum_i Q_i =0. It is noted that the contributions will not be the same due to different masses and couplings, and the question of how anomaly cancellation can occur is raised. The link to a relevant paper is shared, and the possibility of a non-gauge invariant term being added to the Lagrangian is mentioned. It is then explained that the anomaly of the local gauge symmetry cancels due to the charge pattern of matter particles in the Standard Model. The question of whether two diagrams contribute the same is also brought up.
  • #1
ChrisVer
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If I have a triangle diagram for [itex]Z \rightarrow W^-W^+[/itex], do all fermions contribute the same for giving the contraint [itex]\sum_i Q_i =0[/itex]??
I think that eg top quarks will be absent for such a diagram...

any help?
 
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  • #2
Hepth said:
The contributions will not be the same either. Not only do the masses differ, but the couplings to Z as well as the W CKM elements will differ from diagram to diagram.
So how can anomaly cancelation occur if so many things differ?
 
  • #3
I'm not sure now to be honest. I thinks in the limit that the masses are smaller than some higher scale?

http://arxiv.org/pdf/hep-ph/0003143.pdf

Page 6 has some info on it. I'll think about it some until someone else comes along.
 
  • #4
ChrisVer said:
So how can anomaly cancelation occur if so many things differ?

I think the dangerous part contributing to the anomaly in these triangle diagrams is the divergent part. This will force you to add a non gauge invariant term to the bare Lagrangian if it doesn't cancel out. Since the divergent part comes from the UV, the masses don't come in, only the couplings.
 
  • #5
You must have both quarks per family, and you must not forget the color-degeneracy factor. You'll then see that the anomaly of the local gauge symmetry indeed cancels due to the charge pattern of the matter particles in the Standard Model. Without this, it would be obsolete ("not even wrong")!
 
  • #6
No my problem is that:
likeaboss.jpg

Are those two diagrams contributing the same so that they can cancel each other out?
Because I think that [itex]\sum_i Q_i [/itex] is assuming that they do...
 

1. What is an anomaly cancellation triangle?

An anomaly cancellation triangle is a theoretical concept used in particle physics to explain the cancellation of gauge and gravitational anomalies. It involves three particles, one of which is a graviton, and the other two are gauge particles.

2. How does the anomaly cancellation triangle work?

The anomaly cancellation triangle works by balancing the quantum effects of particles with different spin and charges. The triangle must be formed in such a way that the anomalies from each particle cancel each other out, resulting in a consistent and anomaly-free theory.

3. What is the significance of the anomaly cancellation triangle?

The anomaly cancellation triangle is significant because it allows for the consistency of the Standard Model of particle physics. It also provides a framework for studying the behavior of particles at high energies and in extreme conditions, such as those found in the early universe.

4. Can the anomaly cancellation triangle be observed in experiments?

No, the anomaly cancellation triangle is a theoretical concept and cannot be directly observed in experiments. However, its predictions and implications can be tested through experiments and observations of particle interactions.

5. Are there any alternative theories to the anomaly cancellation triangle?

Yes, there are alternative theories to the anomaly cancellation triangle, such as supersymmetry and string theory. These theories also aim to explain the cancellation of anomalies and provide a more complete understanding of the fundamental particles and forces in the universe.

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