$SO(10) \to SU(5) \times U(1)_\chi$ as the Origin of Dark Matter

Abstract

In the decomposition of $SO(10)$ grand unification to $SU(5) \times U(1)_\chi$, two desirable features are obtained with the addition of one colored fermion octet $\Omega$, one electroweak fermion triplet $\Sigma$ 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 $SU(3)_C \times SU(2)_L \times U(1)_Y$ to $SU(5)$, and (2) the automatic (predestined) emergence of dark matter, i.e. $\Omega$, $\Sigma$ and $S$, with dark parity given by $(-1)^{Q_\chi + 2j}$. It suggests that $U(1)_\chi$ may well be the underlying symmetry of the dark sector.