Why Electron & Neutrino Form Doublet in Electroweak Model

[ericthebee]

Hello, I've unfortunately a trivial question, but one I couldn't answer by reading my references.
In the Weinberg-Salam model, why do we take the left electron and neutrino spinors to form a doublet?
I'd like a "physical" answer, if possible, and a more formal one, which I think is based on the SU(2) representations.
My teacher's notes start with writing down a Lagrangian for massless electron and neutrino, and then he literally says "...we must now determine the internal symmetries of the Lagrangian. It's obvious that an internal symmetry must act on particles which have the same space-time properties. The only possibility is then to put together the electron and the neutrino (left parts) in a doublet". Perhaps I'm just too stupid, but it's unintelligible to me.

Thanks everyone :).

 

[Vanadium 50]

You have two particles, so your choices are one doublet or two singlets. Since singlets are uncharged, that eliminates two singlets as a possibility.

 

[Orodruin]

Technically, you could have had them in singlets (anomaly cancelation aside, having them in singlets would mean also putting the quarks in singlets and then there would be no fermions charged under SU(2)). However, this is not what we observe in Nature.

The general idea is to build a Lagrangian which is both Lorentz and gauge invariant.