Dark-sector seeded solution to the strong CP problem

We propose a novel realization of the Nelson-Barr mechanism "seeded'' by a dark sector containing scalars and vector-like quarks. Charge-parity (CP) and a $\mathcal{Z}_8$ symmetry are spontaneously broken by the complex vacuum expectation value of a singlet scalar, leaving a residual $\mathcal{Z}_2$ symmetry that stabilizes dark matter (DM). A complex Cabibbo-Kobayashi-Maskawa matrix arises via one-loop corrections to the quark mass matrix mediated by the dark sector. In contrast with other proposals where non-zero contributions to the strong CP phase arise at the one-loop level, in our case this only occurs at two loops, enhancing naturalness. Our scenario also provides a viable weakly interacting massive particle scalar DM candidate.