Abstract
In the decomposition of $SO(10)$ grand unification to $SU(5)\ifmmode\times\else\texttimes\fi{}U(1{)}_{\ensuremath{\chi}}$, two desirable features are obtained with the addition of one colored fermion octet $\mathrm{\ensuremath{\Omega}}$, one electroweak fermion triplet $\mathrm{\ensuremath{\Sigma}}$ and one complex scalar triplet $S$ to the particle content of the standard model with two Higgs doublets. They are (1) gauge coupling unification of $SU(3{)}_{C}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1{)}_{Y}$ to $SU(5)$, and (2) the automatic (predestined) emergence of dark matter, i.e., $\mathrm{\ensuremath{\Omega}}$, $\mathrm{\ensuremath{\Sigma}}$ and $S$, with dark parity given by $(\ensuremath{-}1{)}^{{Q}_{\ensuremath{\chi}}+2j}$. It suggests that $U(1{)}_{\ensuremath{\chi}}$ may well be the underlying symmetry of the dark sector.
Highlights
The origin of dark matter and the symmetry which maintains it are important issues in particle and astroparticle physics
This is a new realization where the particles added to those of the standard model (SM) are all in the dark sector
It has been proposed in this paper that matter and dark matter are unified under SOð10Þ which breaks to SUð5Þ × Uð1Þχ at MU ∼ 7 × 1016 GeV
Summary
The origin of dark matter and the symmetry which maintains it are important issues in particle and astroparticle physics. Under SUð3ÞC ×SUð2ÞL ×Uð1ÞY ×Uð1Þχ, if the fermions Ω ∼ ð8; 1; 0; 0Þ and Σ ∼ ð1; 3; 0; 0Þ are added together with the scalar S ∼ ð1; 3; 0; −5Þ at the TeV scale, SUð5Þ gauge unification is achieved with MU ∼ 1016 GeV This is a new realization where the particles added to those of the SM are all in the dark sector. The 126 representation of SOð10Þ contains a singlet ζ ∼ ð1; −10Þ under SUð5Þ × Uð1Þχ Such a scalar may be used to break Uð1Þχ at the TeV scale and would allow νc (the righthanded neutrino) to obtain a large Majorana mass, thereby triggering the canonical seesaw mechanism for small. This is usually described as lepton number L breaking to lepton parity ð−1ÞL [16], but here it is clear that it has to do with the breaking of gauge Uð1Þχ to ð−1ÞQχ
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