Feynman diagram for two neutrinos scattering from each other

[newtn46]

Homework Statement

I'm asked to draw a Feynman diagram for two neutrinos scattering from each other.

Homework Equations

None

The Attempt at a Solution

I don't really get the question so I don't know what I'm actually supposed to put in the diagram. Am I supposed to draw a diagram for the neutrino - electron scattering or, for example, a muon decay diagram, where a neutrino and an antineutrino are produced? I don't have problems drawing the diagram, but I don't know which process I should use.

 

[fzero]

What type of diagram would you draw for two electrons scattering from one another?

We're told that we have two neutrinos scattering from one another. This means that the initial state will have 2 neutrinos and no other particles.

Next, it seems to be implied that we should consider elastic scattering, that is the change in energy and momentum of one neutrino is completely accounted for by the corresponding change in the other neutrino. Inelastic scattering means that some energy and momentum is transferred to a 3rd object, such as a nucleus or a new particle created in the collision. If the collision is elastic, then the final state will be two neutrinos and no other particles.

 

[newtn46]

We have done only basic Feynman diagrams, we haven't been told about different types of diagrams. Again, since we haven't been told anything about different types of collision, I assume it is elastic. So "scattering from each other" means that in the intial state I just have two neutrinos? That would mean I would have the same in the final state. The interaction force would be weak, right?

Can't be that simple though...

 

[fzero]

We have done only basic Feynman diagrams, we haven't been told about different types of diagrams. Again, since we haven't been told anything about different types of collision, I assume it is elastic. So "scattering from each other" means that in the intial state I just have two neutrinos? That would mean I would have the same in the final state. The interaction force would be weak, right?

Can't be that simple though...

Well that's why I said to decide what sort of Feynman diagrams contribute to electron-electron scattering. You probably would have covered relevant examples in class. The difference for neutrinos would be determined by the difference in the interaction vertices.

 

[newtn46]

[PLAIN]http://rpmedia.ask.com/ts?u=/wikipedia/commons/thumb/e/e8/Electron-scattering.png/220px-Electron-scattering.png

This is how we would draw it. Thank you very much for your help!

This is not asked for, but I'm curious. Is the interaction force the weak force? If so, which is the force carrier? W+,W- or Z?

 

[fzero]

This is not asked for, but I'm curious. Is the interaction force the weak force? If so, which is the force carrier? W+,W- or Z?

It is the weak force. I don't want to just give the answer away, but I'm also not sure what framework you're working in. By that I mean are you working with interaction terms in a Lagrangian or just given a list of interaction vertices or maybe something else. You should probably review what interaction vertices neutrinos are involved with. If there's any ambiguity, you can also note that electric charge must be conserved at the interaction vertices.

 

[newtn46]

Perfect. Thank you very much!