Investigation of Dark Matter in the 3-2-3-1 Model

We prove that the $SU(3)_Cotimes SU(2)_L otimes SU(3)_Rotimes U(1)_X$ (3-2-3-1) gauge model always contains a matter parity $W_P=(-1)^{3(B-L)+2s}$ as conserved residual gauge symmetry, where $B-L=2(beta T_{8R}+X)$ is a $SU(3)_Rotimes U(1)_X$ charge. Due to the non-Abelian nature of $B-L$, the $W$-odd and $W$-even fields are actually unified in gauge multiplets. We investigate two viab