Simple question on W boson decay products

[adrian52]

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!

 

[mfb]

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?

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

From what I'm reading online it seems like W bosons only decay into electron and anti-electron neutrino pairs

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).

My general approach is that if there is no rule saying it can't work, I assume it does

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

 

[adrian52]

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

 

[Vanadium 50]

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

 

[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.

 

[TEFLing]

... Note that your W is probably virtual, so its final states might be limited (you cannot produce something that violates energy/momentum conservation)...

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 ) ??

 

[TEFLing]

Hi,

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

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

...

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?

 

[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?