Standard Model SU(2) singlets and doublets

[Trixie Mattel]

I know that for SU(2), weak interaction, in the standard model the right handed leptons are singlets, (and right handed neutrinos don't exist).

For right handed quarks are they singlets or doublets in the standard model. So is it (u d)R or is it just u(R) and d(R)

 

[Orodruin]

The right handed quarks are singlets under SU(2). You get quark masses by the Yukawa couplings associated with terms like
$$
\bar Q_L \Phi u_R
$$
where $\Phi$ is the Higgs field - an SU(2) doublet. If $u_R$ was in a doublet, terms like this would not be gauge invariant.

 

[Orodruin]

That being said, in left-right symmetric models, the standard model gauge group is extended by another SU(2) group usually denoted $SU(2)_R$. You can then collect the right-handed fermions in doublets under this new gauge group and promote the Higgs field to a bi-doublet (i.e., a doublet under both SU(2) groups).