Dark matter in a mirror solution to the strong $CP$ problem

We study thermal production of dark matter (DM) in a realization of the minimal models of Bonnefoy et al. [Phys. Rev. Lett. 131, 221802 (2023)], where parity is used to solve the strong $CP$ problem by transforming the entire Standard Model (SM) into a mirror copy. Although the mirror electron $e^{\prime }$ is a good DM candidate, its viability is mired by the presence of the mirror up quark $u^{\prime }$, whose abundance is intimately related to the $e^{\prime }$ abundance and must be suppressed. This can be achieved through a sequential freeze-in mechanism, where mirror photons are first produced from SM gluons, and then the mirror photons produce $e^{\prime }$. After computing the details of this double freeze-in, we discuss the allowed parameter space of the model, which lies at the threshold of experimental observations. We find that this origin of $e^{\prime }$ DM requires a low reheating temperature after inflation and is consistent with the baryon asymmetry arising from leptogenesis, providing mirror neutrinos have a significant degeneracy. Finally, we show that this $e^{\prime }$ DM is not compatible with Higgs parity, the simplest scheme with exact parity, unless SM parameters deviate significantly from their central values or the minimal model is extended.