Three level Feynman diagramas lagrangian density

[pstq]

Hi,
I am trying to figure out how to draw all the three level Feynman diagrams corresponding to this lagrangian density 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
for this process F+ \bar{F} → F+ \bar{F}
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 \phi^3 three Feynman diagrams, whose vertex are proportional to
\eta^2
for \phi^4 another three , is that right ?

the problem is that I think that we don't have u channel in the \phi^3 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, \psi 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 F+ \bar{F} → F+ \bar{F} or not?

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

thanks !

 

[pstq]

this is not coursework questions nor homework per se, so I hope this is the right place to post this. In case I am wrong , my sincerest apologies

 

[The_Duck]

I am trying to figure out how to draw all the three level Feynman diagrams

I guess you mean *tree* level?

for this process F+ \bar{F} → F+ \bar{F}

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 $F + F \to F + F$?

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 \phi^3 three Feynman diagrams, whose vertex are proportional to
\eta^2
for \phi^4 another three , is that right ?

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.

the problem is that I think that we don't have u channel in the \phi^3 case, but I am not sure why .

There is definitely a u channel diagram.

and another question, \psi 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 F+ \bar{F} → F+ \bar{F} or not?

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.

 

[ChrisVer]

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

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

For the last term, #2 post is totally right...

 

[pstq]

thanks a lot :):):)