Hello, I've been reading about the weak interaction. Basically, the weak interaction couples to particles that are left-handed, and we introduce the electron-electron neutrino as a (left-handed) SU(2) doublet. So, the gauge bosons (W+, W-, and Z) transform SU(2) triplet. Am I right? So...my question is...why do we enlarge the gauge group to SU(2)×U(1)? And what transforms in U(1)?