Asymmetric dark matter from semi-annihilation: unitarity constraints and long-lived final states

This work presents an asymmetric dark matter model with relic density determined by the freeze-out of asymmetric semi-annihilations into long-lived particles slowly decaying into the Standard Model states. We carefully consider the $CPT$ symmetry and unitarity constraints to the asymmetries entering the Boltzmann equation. The main idea of the paper is to point out a critical inconsistency in the previous literature, where these constraints are violated. We present a systematic approach to avoid the inconsistency.