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It is shown that for a higher weak isospin symmetry, $SU(P)_L$ with $Pgeq 3$, the baryon minus lepton charge $B-L$ neither commutes nor closes algebraically with $SU(P)_L$ similar to the electric charge $Q$, which all lead to a $SU(3)_Cotimes SU(P)_Lotimes U(1)_Xotimes U(1)_N$ gauge completion, where $X$ and $N$ determine $Q$ and $B-L$, respectively. As a direct result, the neutrinos obtain appropriate masses via a canonical seesaw. While the version with $P=3$ supplies the schemes of single-component dark matter well established in the literature, we prove in this work that the models with $Pgeq 4$ provide the novel scenarios of multicomponent dark matter, which contain simultaneously at least $P-2$ stable candidates, respectively. In this setup, the multicomponet dark matter is nontrivially unified with normal matter by gauge multiplets, and their stability is ensured by a residual gauge symmetry which is a remnant of the gauge symmetry after spontaneous symmetry breaking. The thr
It is well established that the $SU(P)_L$ gauge symmetry for $Pgeq 3$ can address the question of fermion generation number due to the anomaly cancellation, but it neither commutes nor closes algebraically with electric and baryon-minus-lepton charge
Standard Model with right handed neutrinos charged under additional $U(1)_{B-L}$ gauge symmetry offer solutions to both dark matter (DM) problem and neutrino mass generation, although constrained severely from relic density, direct search and Higgs v
We argue that neutrino mass and dark matter can arise from an approximate $B-L$ symmetry. This idea can be realized in a minimal setup of the flipped 3-3-1 model, which discriminates lepton families while keeping universal quark families and uses onl
To enforce the conservation of baryon number B and not lepton number L in supersymmetry, a new U(1)_X gauge symmetry is recommended. An example is offered with new particles interacting under U(1)_X which are good candidates for the dark matter of the Universe.
The present matter content of our universe may be governed by a $U(1)_{B-L}$ symmetry -- the simplest gauge completion of the seesaw mechanism which produces small neutrino masses. The matter parity results as a residual gauge symmetry, implying dark