- #1
pstq
- 10
- 0
Hi,
I am trying to figure out how to draw all the three level Feynman 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 !
I am trying to figure out how to draw all the three level Feynman 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 !