Understanding the W Decay Branching Ratio to Quarks & Gluons

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Discussion Overview

The discussion revolves around the branching ratio of W boson decay to quarks and gluons, specifically addressing the inclusion of processes like ##W \to q \bar{q'}## and ##W \to q \bar{q'}g##. Participants explore the implications of these decay modes within the context of quantum field theory (QFT) and Feynman diagrams.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the relevance of gluon emission in the context of W decay, suggesting that gluons are produced later and do not pertain to the W properties.
  • Another participant argues that the concept of "later" is ambiguous in Feynman diagrams, indicating that calculations would include earlier gluon emissions and that high-energy gluon emissions can lead to three jets instead of two.
  • A participant expresses confusion regarding the use of "1 particle irreducible" (1PI) diagrams, stating that the diagram presented is not 1PI and discussing the implications for understanding the Wqq vertex.
  • Another participant challenges the understanding of 1PI, clarifying that it pertains to propagators and not interaction diagrams, and emphasizes the need to focus on interaction diagrams without 1PIs on the external legs.
  • One participant raises the question of whether the focus should be on understanding vertices involving W or the decays of W itself.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the interpretation of Feynman diagrams, the relevance of gluon emissions in W decay processes, and the application of 1PI concepts. The discussion remains unresolved with multiple competing views presented.

Contextual Notes

Participants reference specific concepts from quantum field theory, such as Feynman diagrams and 1PI, which may require further clarification or context for those less familiar with the terminology.

kelly0303
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Hello! In Modern Particle Physics by Mark Thomson, in the Electroweak Unification chapter, pg. 412 he talks about the branching ration of the W decay to quarks. And for this he includes both the ##W\to q \bar{q'}## and ##W\to q \bar{q'}g## i.e. the state with a gluon and 2 quarks in the final state. I am not sure I understand this. Isn't the decay defined just at the W vertex? The gluon is produced later by the quark and it has nothing to do with the W properties. Also, one can have a photon, too coming out of the quark and even in the leptonic case, one can have a photon emission by one of the leptons resulting from the decay. Why is it just this gluon case considered? Thank you!
 
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"Later" is not a well-defined concept if it happens in the same Feynman diagram. If you calculate it your integral will also run over an "earlier" gluon emission.
The quarks will hadronize in some way afterwards anyway, but you can also have the emission of a gluon with a high energy - in that case you get three jets instead of two. Photon emission is possible as well, it is relatively rare as the electromagnetic interaction is much weaker.
 
mfb said:
"Later" is not a well-defined concept if it happens in the same Feynman diagram. If you calculate it your integral will also run over an "earlier" gluon emission.
The quarks will hadronize in some way afterwards anyway, but you can also have the emission of a gluon with a high energy - in that case you get three jets instead of two. Photon emission is possible as well, it is relatively rare as the electromagnetic interaction is much weaker.
I am sorry, I am still confused. The diagram he shows, is not "1 particle irreducible" (1PI). I remember from my QFT class that, when trying to understand a process, one looks only at diagrams that't can't be split into 2 or more diagrams (and this one can). For example, one can add lots of self interactions on the quark propagator, but that doesn't contribute to the Wqq vertex. Of course Wqq is just a first order approximation, but but higher order must still be 1PI, while W->qqg is not.
 
kelly0303 said:
I am sorry, I am still confused. The diagram he shows, is not "1 particle irreducible" (1PI). I remember from my QFT class that, when trying to understand a process, one looks only at diagrams that't can't be split into 2 or more diagrams (and this one can). For example, one can add lots of self interactions on the quark propagator, but that doesn't contribute to the Wqq vertex. Of course Wqq is just a first order approximation, but but higher order must still be 1PI, while W->qqg is not.
I do not think you have understood what 1PI means and when it is used. It is used in connection to propagators, not interaction diagrams. What you want is the interaction diagram with no 1PIs on the external legs. The leg with the extra gluon is not a 1PI because it has three legs. A 1PI only has two legs, the ”incoming” and ”outgoing” particle.
 
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That depends on the process you want to understand. Do you want to understand vertices with W or do you want to understand W decays?
 
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