Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Three level Feynman diagramas lagrangian density

  1. Nov 17, 2014 #1
    Hi,
    I am trying to figure out how to draw all the three level Feynmann diagrams corresponding to this lagrangian density [tex] L = \frac{1}{2} \partial _{\mu} \phi \partial^{\mu} \phi - \frac{\mu^2}{2}\phi^2- \frac{\eta}{3!}\phi^3-\frac{\lambda}{4!} \phi^4+i \bar{\psi} \gamma _{\mu} \partial^{\mu} \psi \phi -m \bar{\psi} \psi+ig \bar{\psi} \gamma^{5} \psi \phi [/tex]
    for this process [tex] F+ \bar{F} → F+ \bar{F} [/tex]
    and φ is the field associated to this particle F.

    So i was thinking on drawing the 3 Feynman diagram (i.e. u, s,t channels ) for every interaction term . I mean

    for the interaction [tex] \phi^3 [/tex] three Feynman diagrams, whose vertex are proportional to
    [tex] \eta^2 [/tex]
    for [tex] \phi^4 [/tex] another three , is that right ?

    the problem is that I think that we don't have u channel in the [tex] \phi^3 [/tex] case, but I am not sure why . So if someone could enlighten me about this as well, you will make another fellow human interested in particle physics very happy today.



    and another question, [tex] \psi [/tex] is the dirac spinor for another particle X which is not F, would i need to take into account the last term of the above Lagrangian which is interaction term between the particles F and the others , if I am considering only the above process [tex] F+ \bar{F} → F+ \bar{F} [/tex] or not?

    Any help with any question/ or any remark would be highly appreciated

    thanks !
     
  2. jcsd
  3. Nov 17, 2014 #2
    this is not coursework questions nor homework per se, so I hope this is the right place to post this. In case Im wrong , my sincerest apologies
     
  4. Nov 17, 2014 #3
    I guess you mean *tree* level?

    From your Lagrangian, it looks like ##\phi## is a real scalar field. So the F particle is its own antiparticle. So I guess you are considering ##F + F \to F + F##?

    The ##\phi^3## interaction produces three tree-level diagrams, corresponding to the u, s, and t channels. However the ##\phi^4## interaction produces only one tree-level diagram for the process you are interested in.

    There is definitely a u channel diagram.

    The X particle will only matter if you consider loop diagrams. Since there are no X's in the initial and final states, they can only appear in loops.
     
  5. Nov 17, 2014 #4

    ChrisVer

    User Avatar
    Gold Member

    It's better to ask yourself why don't you see a u-channel for [itex] \phi [/itex]? (however you saw a t-channel)

    For [itex] \phi^4 [/itex] you will only get the diagram that looks like this: X
    for 4 external legs...

    For the last term, #2 post is totally right...
     
  6. Nov 22, 2014 #5
    thanks a lot :):):)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Three level Feynman diagramas lagrangian density
Loading...