# Simple question on W boson decay products

1. Mar 8, 2015

Hi,

I'm working on an assignment in which the following reaction takes place:

$$\nu_e e^- \rightarrow \nu_e e^-$$

And I'm wondering whether its possible to have an electron neutrino and an electron annihilate to form a $$W^-$$ boson, after which that boson decays into a $$\nu_e e^-$$ pair, satisfying the equation? From what I'm reading online it seems like W bosons only decay into electron and anti-electron neutrino pairs, but I figure as long as the lepton number is being conserved (which it is in the above reaction), I don't see any rule stating why it can't work.

My general approach is that if there is no rule saying it can't work, I assume it does (I don't have any other way to operate to be honest). As far as I know I only have to worry about conservation of angular momentum, charge, baryon number, and lepton number for the reactions we're considering (this is all undergraduate level).

Thanks for the help!

2. Mar 8, 2015

### Staff: Mentor

Sure.
It is not the only reaction mechanism, however.

That is not true, decays to quarks are possible as well. Note that your W is probably virtual, so its final states might be limited (you cannot produce something that violates energy/momentum conservation).

That is the general idea, and it works for all processes. Just keep in mind some reactions can be extremely rare.

3. Mar 8, 2015

Thank you, that was very helpful. As a side note let me just say I am really enjoying drawing these Feynman diagrams! :D

Also I was a bit sloppy I think I should not have written 'only', I meant to say in the context of the electron lepton only. Because of course it can decay into muons and tauons and quarks like you said

4. Mar 8, 2015

Staff Emeritus
Don't you want these to be anti-neutrinos?

5. Mar 10, 2015

### ChrisVer

You can have W only as scattering (not s-channel)...Otherwise they will either not interact at all, or they can scatter with some Z0.

6. Mar 10, 2015

### TEFLing

A virtual weak boson... Represents the transmission of the forces of the weak interaction... Of the pair of particles...

And is like a virtual photon for EM ( vs. a real actual live full fledged photon existing on its own, describable by a potentially eternal wave function ) ??

7. Mar 10, 2015

### TEFLing

Is this an interaction where the electron charge is transferred to the neutrino, so that the neutrino is "charged" into an electron... And the electron "discharged" into a neutrino... I.e. They swap roles ?

Or is this a scattering reaction only, where spatial momentum in xyz is transferred via the weak force?

8. Mar 10, 2015

### TEFLing

Can virtual bosons have off shell SPIN? Would an electron which emits a virtual W boson necessarily spin flip? Would the neutrino need to spin flip to absorb the W? Or could a virtual boson have any energy momentum and angular momentum?