The neutrino and electroweak transformations

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!

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.

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.