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Three level Feynman diagramas lagrangian density

  1. Nov 17, 2014 #1
    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


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    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 :):):)
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