$SO(10)\to SU(5)\times U(1{)}_{\chi }$ 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.

Comments: 15 pages, 1 figure, references added, discussion expanded (revised numbers after publication)