Investigation of dark matter in the 3-2-3-1 model

Abstract

We prove that the $SU(3{)}_{C}\ensuremath{\bigotimes}SU(2{)}_{L}\ensuremath{\bigotimes}SU(3{)}_{R}\ensuremath{\bigotimes}U(1{)}_{X}$ (3-2-3-1) gauge model always contains a matter parity ${W}_{P}=(\ensuremath{-}1{)}^{3(B\ensuremath{-}L)+2s}$ as conserved residual gauge symmetry, where $B\ensuremath{-}L=2(\ensuremath{\beta}{T}_{8R}+X)$ is a $SU(3{)}_{R}\ensuremath{\bigotimes}U(1{)}_{X}$ charge. Due to the non-Abelian nature of $B\ensuremath{-}L$, the $W$-odd and $W$-even fields are actually unified in gauge multiplets. We investigate two viable versions for dark matter according to $\ensuremath{\beta}=\ifmmode\pm\else\textpm\fi{}1/\sqrt{3}$, 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.