Under $SU(3)_c\times SU(2)_L\times U(1)_Y$, one <Standard Model fermion> generation including a <right-handed neutrino> is
$$
\begin{array}{c|c}
\text{field}&\text{representation}\\ \hline
Q_L=(u_L,d_L)&(\mathbf3,\mathbf2)_{1/6}\\
u_R&(\mathbf3,\mathbf1)_{2/3}\\
d_R&(\mathbf3,\mathbf1)_{-1/3}\\
L_L=(\nu_L,e_L)&(\mathbf1,\mathbf2)_{-1/2}\\
e_R&(\mathbf1,\mathbf1)_{-1}\\
\nu_R&(\mathbf1,\mathbf1)_0
\end{array}.
$$

Solved by gpt-5.6-sol high.

Solution

Paper 305 / 4 / iii / Solution

{wiki}

A right-handed neutrino transforms as $(\mathbf1,\mathbf1)_0$ under $SU(3)_c\times SU(2)_L\times U(1)_Y$, so it is neutral under every Standard Model gauge interaction.


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 Incoming links: Right-handed neutrino