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.
Highlights
The standard model is very successful, but it is not a complete theory as it fails to address the existence of nonzero small neutrino masses and neutrino mixing [1] as well as the presence of dark matter that occupies roundly 26% mass-energy density of the Universe [2]
We would like to search for a stabilizing mechanism by virtue of a noncommutative B − L gauge symmetry that uniquely determines dark matter from the known normal matter as forming an irreducible gauge multiplet by symmetry principles. This is in sharp contrast to the usual global and Abelian B, L, B − L extensions of the standard model, including the minimal left-right symmetric model
There is no mixing between the ordinary and new quarks due to the matterparity conservation. It means the interactions of the flavor-changing neutral currents (FCNCs) with H2, Z0R do not depend on the way of the symmetry breaking, but the amplitudes of the induced effective FCNC interactions do, set by H2, Z0R masses
Summary
We would like to search for a stabilizing mechanism by virtue of a noncommutative B − L gauge symmetry that uniquely determines dark matter from the known normal matter as forming an irreducible gauge multiplet (dark matter, normal matter) by symmetry principles This is in sharp contrast to the usual global and Abelian B, L, B − L extensions of the standard model, including the minimal left-right symmetric model. The B − L-charged scalar field breaks the 3-2-3-1 symmetry, defining both the seesaw scale as the scalar vacuum value producing small neutrino masses and the matter parity WP 1⁄4 ð−1Þ3ðB−LÞþ2s as residual SUð3ÞR ⊗ Uð1ÞX gauge symmetry responsible for dark matter stability.
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