# The neutrino and electroweak transformations

1. Apr 15, 2012

### ryanwilk

Hi, quick question.

"In electroweak theory, the neutrino belongs to an SU(2) doublet"

So, does the neutrino belong to an SU(2)xU(1) (electroweak) doublet or just SU(2)?

Thanks!

Last edited: Apr 15, 2012
2. Apr 15, 2012

### Bill_K

The left-handed neutrino and left-handed electron form an electroweak SU(2)xU(1) doublet. The right-handed electron forms an electroweak singlet. The right-handed neutrino, if it exists, also forms a singlet.

3. Apr 15, 2012

### The_Duck

It's possible to speak of a particle's transformation properties under SU(2) and U(1) separately. Under SU(2) transformations the neutrino transforms as part of a doublet. Under U(1) transformations the neutrino picks up a phase proportional to its hypercharge. So I think it's most correct to say "SU(2)" double instead of "SU(2) x U(1)" doublet.