• #1
MyName
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Homework Statement


Consider four real massive scalar fields, [itex]\phi_1,\phi_2,\phi_3,[/itex] and [itex]\phi_4[/itex], with masses [itex]M_1,M_2,M_3,M_4[/itex].
Let these fields be coupled by the interaction lagrangian [itex]\mathcal{L}_{int}=\frac{-M_3}{2}\phi_1\phi_{3}^{2}-\frac{M_4}{2}\phi_2\phi_{4}^{2}[/itex].
Find the scattering amplitude for [itex]\phi_{3}\phi_{4}\rightarrow\phi_3\phi_4[/itex], to tree level.

Homework Equations


I'm not really sure what to put here.

The Attempt at a Solution


This honestly looks like a trick question to me. The first step is obviously to write down the relevant feynman diagrams and feynman rules to evaluate them, but I can't find a single tree level diagram for this process. A diagram would need an incoming [itex]\phi_3[/itex] and an incoming [itex]\phi_4[/itex], as well as an outgoing [itex]\phi_3[/itex] and an outgoing [itex]\phi_4[/itex].
The interaction lagrangian makes me think that we should have a vertex between a [itex]\phi_1[/itex] and two [itex]\phi_3[/itex]'s, as well as a vertex between a [itex]\phi_2[/itex] and two [itex]\phi_4[/itex]'s, but this still doesn't allow [itex]\phi_3[/itex] and [itex]\phi_4[/itex] to interact.
Perhaps I am misunderstanding the meaning of tree level (I think it just means one of each type of interaction vertex), or perhaps I am just misunderstanding the interactions.
Could this possibly have to do with interactions via the kinetic terms of the lagrangian? Can a tree level diagram just consist of the [itex]\phi_3[/itex] and the [itex]\phi_4[/itex] propagating along and not interacting (if yes I don't think this would contribute to the scattering), I'm not sure and would appreciate any help. I'm just feeling pretty confused at the moment.
Thanks!
 
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  • #2
With that Lagrangian the 13 and 24 sectors do not mix.
 
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  • #3
Thanks, I thought that was the case and really appreciate the confirmation.
 

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