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

[Crosshash]

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

e^+ e^- \rightarrow \tau^+ \tau^-
ie
[PLAIN]http://hepwww.rl.ac.uk/OpenDays98/Century%20of%20electrons/images/tt_f.gif
and be like "yep, a Z^0 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
"W changes neutrinos into non neutrinos"
and
"\gamma only interacts with charged particles, Z^0 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? :( )

 

[vanhees71]

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 \tau^+ \tau^- can be "mediated" by both a photon or a Z boson. That's why you label the internal line with a Z^0.

 

[Crosshash]

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?

 

[James50]

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^- -> \upsilon_e\overline{\upsilon}_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.

 

[The_Duck]

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.