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

Abstract: We prove that the $SU(3)C\otimes SU(2)_L \otimes SU(3)_R\otimes U(1)_X$ (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 $SU(3)_R\otimes U(1)_X$ 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 viable versions for dark matter according to $\beta=\pm1/\sqrt{3}$, where the dark matter candidates can be fermion, scalar, or vector fields. We figure out the parameter spaces in the allowed regions of the relic density and direct detection cross-sections. Additionally, we examine the neutrino masses induced by the seesaw mechanism along with associated lepton flavor violation processes. The new gauge boson searches at the LEPII and LHC are discussed.