Pati-Salam charge embedding ($Q=T_{3L}+T_{3R}+(B-L)/2$)

The charge relation combines left and right weak isospin with the generator distinguishing quarks from leptons inside the extended color charge group.

For the right-handed neutrino, $T_{3R}=1/2$ and $B-L=-1$, so $Y=T_{3R}+(B-L)/2=0$. Its colour-singlet and left-weak-singlet assignments make it sterile under the Standard Model after symmetry breaking.