Anomaly cancellation triangle

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    Anomaly Triangle
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Discussion Overview

The discussion revolves around the anomaly cancellation in triangle diagrams related to the process Z → W^-W^+. Participants explore whether all fermions contribute equally to the constraint ∑i Qi = 0 and the implications of differing masses and couplings on this cancellation.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions if all fermions contribute equally to the anomaly cancellation condition ∑i Qi = 0, suggesting that top quarks may be absent from the diagram.
  • Another participant argues that contributions will not be the same due to differences in masses and couplings, raising concerns about how anomaly cancellation can occur under these conditions.
  • A different participant expresses uncertainty, proposing that anomaly cancellation might hold in the limit where masses are smaller than some higher scale, referencing an external document for further information.
  • One participant emphasizes that the divergent part of the triangle diagrams is critical for understanding anomaly contributions, suggesting that it forces the addition of non-gauge invariant terms if not canceled out.
  • Another participant asserts that both quarks per family must be included and highlights the importance of the color-degeneracy factor in ensuring that the anomaly cancels due to the charge pattern of matter particles in the Standard Model.
  • A participant raises a specific concern about whether two diagrams contribute equally to the anomaly cancellation, questioning the assumption that ∑i Qi is valid under these circumstances.

Areas of Agreement / Disagreement

Participants express differing views on the contributions of fermions to anomaly cancellation, with no consensus reached on whether all contributions are equal or how the differences affect the cancellation process.

Contextual Notes

Participants note the complexity introduced by differing masses and couplings, as well as the role of divergent parts in the diagrams, but do not resolve these issues or clarify assumptions regarding the conditions for anomaly cancellation.

ChrisVer
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If I have a triangle diagram for Z \rightarrow W^-W^+, do all fermions contribute the same for giving the contraint \sum_i Q_i =0??
I think that eg top quarks will be absent for such a diagram...

any help?
 
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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?
 
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.
 
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.
 
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")!
 
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 \sum_i Q_i is assuming that they do...
 

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