A new idea for relating the asymmetric dark matter mass scale to the proton mass

Asymmetric dark matter is a well-motivated approach to explain the apparent coincidence between the relic densities of visible and dark matter, ${\mathrm{\Omega }}_D\simeq 5.4{\mathrm{\Omega }}_b$. A complete explanation requires two components, a relation between the particle masses of the dark and visible matter, and a second relation between the number densities in each sector. In this work, we propose a new mechanism to address the former. We consider an extended $SU(3{)}_1\times SU(3{)}_2$ colour group in the visible sector, with QCD embedded as the diagonal subgroup. A ${\mathbb{Z}}_2$ exchange symmetry then relates $SU(3{)}_2$ to a dark, confining $SU(3{)}_D$ sector. The dark matter is a composite state of dark fermions transforming in the fundamental representation of $SU(3{)}_D$. The spontaneously broken ${\mathbb{Z}}_2$ symmetry ultimately leads to a relation between the QCD and dark gauge couplings which, for suitable field content, gives rise to confinement scales of the same order of magnitude. The mechanism leads to a rich particle spectrum above the TeV scale which could be probed at future experiments. The model also naturally includes an axion solution to the strong CP problem.