gauge group being $SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$. The charge of a particle in this model is defined as $$\mathcal{Q}=I_{3L}+I_{3R}+\frac{B-L}{2},$$ where $I_{3L/3R}$ is the third component of isospin under $SU(2)_{L/R}$ symmetry. The quarks and leptons consist of three generation of left-handed and right-handed doublet fields: $$\begin{aligned}
\!\!Q_L\left (3,2, 1, \frac13 \right )\!\!&=&\!\!\left (\begin{array}{c}
u\\ d \end{array} \right )_L,~~
Q_R \left( 3,1, 2, \frac13 \right )\!=\!\left (\begin{array}{c}
u\\d \end{array} \right )_R ,\nonumber \\
l_L \left ( 1,2, 1, -1 \right )&=&\left (\begin{array}{c}
\nu\\ e\end{array}\right )_L,~~
l_R\left ( 1,1, 2, -1 \right )=\left (\begin{array}{c}
\nu \\ e \end{array}\right )_R,~~~\end{aligned}$$ where the numbers in the brackets denote the quantum numbers under $SU(3)_C$, $SU(2)_L$, $SU(2)_R$, $U(1)_{B-L}$ gauge groups respectively. Here we see that the right-handed neutrinos are naturally present due to the gauge symmetry of the models.

The minimal Higgs sector, required for a consistent symmetry breaking mechanism and generation of quark and lepton masses and mixing angles, consists of $$\begin{aligned}
H_R(1,1,2,1)&=&\left (\begin{array}{c}
H_R^+ \\H_R^0 \end{array} \right ),~~
H_L(1,2,1,1)=\left (\begin{array}{c}
H_L^+ \\H_L^0 \end{array} \right ),~~
\Phi(1,2,2,0)={\left (\begin{array}{cc}
\phi^{0}_1 & \phi^{+}_{2} \\ \phi^{-}_{1} & \phi^{0}_{2} \end{array} \right )},~~ \delta(1,1,1,2) = \delta^+ .~~~~~\end{aligned}$$ The right-handed doublet field $H_R$ is required for breaking the $SU(2)_R 