Quark seesaw mechanism, dark $U(1)$ symmetry, and the baryon-dark matter coincidence

We attempt to understand the baryon-dark matter coincidence problem within the quark seesaw extension of the standard model where parity invariance is used to solve the strong $CP$ problem. The $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$ gauge symmetry of this model is extended by a dark $U(1{)}_X$ group plus inclusion of a heavy neutral vector-like fermion ${\chi }_{L,R}$ charged under the dark group which plays the role of dark matter. All fermions are Dirac type in this model. Decay of heavy scalars charged under $U(1{)}_X$ leads to simultaneous asymmetry generation of the dark matter and baryons after sphaleron effects are included. The $U(1{)}_X$ group not only helps to stabilize the dark matter but also helps in the elimination of the symmetric part of the dark matter via $\chi -\overline{\chi }$ annihilation. For dark matter mass near the proton mass, it explains why the baryon and dark matter abundances are of similar magnitude (the baryon-dark matter coincidence problem). This model is testable in low threshold (sub-keV) direct dark matter search experiments.