How can you determine which bosons are used in reactions in QFT?

In summary: This is something that is definitely not explicit in the literature. There are a few hints, though. For example, in the textbooks on QCD there is a section on decoupling of W and Z. Basically, if you have a process with a lot of W and Zs, and you want to figure out how many Ws and Zs are involved, you can look at the lepton number. If there are a lot of Ws and Zs, then the lepton number is going to be high.
  • #1
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Hey there, this isn't a homework / coursework question so I didn't think it should be posted in that section.

I can't seem to find a source which explicitly tells you how to determine which bosons are used in reactions.

I understand how to work out if a reaction is legal or not by using charge conservation and lepton number conservation. I also understand why virtual particles exist and which particles are on shell or off shell. - atleast I think I do.

But what i don't understand, is how someone can look at a process such as

[tex]e^+ e^- \rightarrow \tau^+ \tau^-[/tex]
ie
[PLAIN]http://hepwww.rl.ac.uk/OpenDays98/Century%20of%20electrons/images/tt_f.gif [Broken]
and be like "yep, a [tex]Z^0[/tex] is here".

I know it can be seen if you have the interaction lagrangian is present but when this is not the case, are there certain rules you can use?

My notes have little bits like
"[itex]W[/itex] changes neutrinos into non neutrinos"
and
"[tex]\gamma[/tex] only interacts with charged particles, [tex]Z^0[/tex] if they're non charged" (which doesn't seem right with the example process I gave)

So are there some basic rules I can remember so I will always be able to atleast determine the boson correctly?

Much appreciated

(and why are my Latex tags not working? :( )
 
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  • #2
It's clear that Feynman diagrams don't make sense, if you don't tell what model you are working with. E.g., your electron-positron annihilation to [itex]\tau^+ \tau^-[/itex] can be "mediated" by both a photon or a Z boson. That's why you label the internal line with a [itex]Z^0[/itex].
 
  • #3
Yeah, okay, so I could use a photon or a Z for that interaction. So would it be accurate to say both diagrams would contribute to the probability amplitude?
 
  • #4
The Z and W+/-, being of the weak interaction, have a smaller cross section than the electromagnetic interaction - so particle annhiliation then reproduction of the same particles are normally by a photon (it can, of course, be by the Z0, it's just that it happens far less often). However, the only way of producing a neutrino is via the weak. So if you had, for example, e+e- -> [tex]\upsilon[/tex]e[tex]\overline{\upsilon}[/tex]e Then the Z0 would have to be used. The reason you would use the W+/- would be if there were charge changes involved.

Basically for Feynman diagrams, you go through the order, starting from gluon(s), then photons, then W and Z. Starting with the strong, if the normal Feynman line from initial quark to end quark can be unbroken, without breaking any rules of conservation, that is the diagram you would draw and label it as strong. Then, if the line must be broken but can still be mediated by a gluon (it's still strong, it's just that there no way for a quark to get into its final state directly), then 3 gluons must be used to conserve parity and colour neutrality. This is suppressed due to a lower coupling constant. Then if strong can't be used, you go through to a photon, and if that can't be used, you go to weak, deciding which to be used based on conservation of charge.
 
  • #5
To calculate an amplitude of some process in QFT you write down ALL diagrams that contribute to that process and add them up. Of course this is an infinite series of diagrams, so you generally just take a finite number of diagrams to get an approximation to the amplitude. For example you can take only the tree-level diagrams and ignore the ones with loops, which generally contribute less. To know what sort of diagrams you can write down you need a list of what vertices there are in the theory, which as you mention you can read off the interaction term in the Lagrangian. In the case of e+e- -> tau+tau- there are two tree-level diagrams: one going through a photon and one going through a Z, which you should add together. At low energies the Z diagram is much less important because the Z mass is large, so you might neglect it depending on what accuracy you desire.
 

1. What are Feynman diagrams and why are they important in science?

Feynman diagrams are visual representations of mathematical equations used to describe interactions between subatomic particles in quantum field theory. They are important because they provide a clear and intuitive way to understand and calculate complex interactions between particles, allowing for more accurate predictions and interpretations of experimental results.

2. How do Feynman diagrams work?

Feynman diagrams use lines and vertices to represent particles and their interactions. The lines represent the paths of particles, while the vertices represent the points where particles interact. By following the lines and vertices, one can determine the probability of a particular outcome for a given interaction.

3. What is the significance of the direction of the lines in a Feynman diagram?

The direction of the lines in a Feynman diagram represents the flow of time. Particles traveling forward in time are represented by solid lines, while those traveling backwards in time are represented by dashed lines. This allows for a visual understanding of the cause-and-effect relationships between particles in an interaction.

4. How do I draw a Feynman diagram?

To draw a Feynman diagram, you will need to first determine the type of interaction you are trying to represent (e.g. electron-positron annihilation). Then, use the Feynman diagram rules to determine the number and type of lines and vertices needed. Finally, draw the diagram with accurate placement and labeling of particles and interactions.

5. What are some common mistakes to avoid when drawing Feynman diagrams?

Some common mistakes to avoid when drawing Feynman diagrams include using incorrect line and vertex types, improperly labeling particles, and not following the correct flow of time. It is also important to accurately represent the conservation of energy and momentum in an interaction. Additionally, make sure to double-check your diagram for any missing or unnecessary lines or vertices.

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