Weak Interaction-QED Interactions

[Morgoth]

Well, I was looking at the beta decay of neutron, and I thought that the weak interaction can be seen in analogue to QED, where you have an electron that emits(or absorbs) a photon and gets scattered.
In the same way, couldn't we say that a Neutron is scattered to a Proton (I see them as the same particle- Nucleon) by emittion of electron+antineutronio?
So the electron and electron antineutrino could play the role that photon does, without needing to insert the intermediative bosons... How could I oppose that?

One idea that I had is the mass and the interaction range... But I'm open to suggestions...

 

[The_Duck]

Fermi initially proposed a theory of the weak interactions in which the neutron directly couples to the electron, electron antineutrino, and proton through a zero-range interaction with no intermediate W boson. This works, except that the resulting quantum field theory is not renormalizable and so is only useful below some energy scale. That's to be expected of course, since there really is a vector boson. When you get up to energies near the vector boson mass this fact becomes obvious and any theory neglecting it will make wrong predictions.

 

[kevinferreira]

The Duck already told eveything with great precision, I just wanted to add that one of the deepest problems of Fermi 4-fermion interaction is unitarity violation, which ultimately led theorists to consider intermediate bosons.

 

[Bill_K]

Fermi initially proposed a theory of the weak interactions in which the neutron directly couples to the electron, electron antineutrino, and proton through a zero-range interaction with no intermediate W boson. This works, except that the resulting quantum field theory is not renormalizable and so is only useful below some energy scale.

Right, but you can't stop there. Even with the W boson included, the theory is still nonrenormalizable. To get a theory that is renormalizable you must also add the Higgs.

 

[Morgoth]

thanks for the rest information, however I can't get how the insertion of a Vector Boson instead of the (νe,e) can help in any way... I'm not trying to say that Fermi was right (of course nowadays the Bosons of WI have been observed, so even experimentally they are verified). I am trying to think/understand how, without knowing a priori if they exist, you put them in your theory... So, when they did it, they should have a theoretical problem that the W,Z would solve...

I guess the unitarity violation is interesting, do you have any source about it I can check?

 

[kevinferreira]

thanks for the rest information, however I can't get how the insertion of a Vector Boson instead of the (νe,e) can help in any way... I'm not trying to say that Fermi was right (of course nowadays the Bosons of WI have been observed, so even experimentally they are verified). I am trying to think/understand how, without knowing a priori if they exist, you put them in your theory... So, when they did it, they should have a theoretical problem that the W,Z would solve...

I guess the unitarity violation is interesting, do you have any source about it I can check?

I don't have any concrete source, sorry, I studied this with my lecture notes. But I think any weak/electroweak interaction theory book should have this explained.
You see, unitarity constraints the S-matrix in terms of available energy s. The 4-fermion interaction violates this constraint at high energies. The idea of a W boson permits to get this constraint back on. Then another problem arises, as the W bosons give you new kinds of interaction, new Feynman diagrams (at tree level), which on their turn violate unitarity again at even higher energies. So the same idea comes up and the Z boson is introduced. And that's it.

 

[Bill_K]

Here's a good discussion of it in a Google Book, "Introduction to Electroweak Unification", in the sections titled "Difficulties of Fermi Theory" and "Intermediate Vector Boson".