Classification of dark pion multiplets as dark matter candidates and collider phenomenology

New confining sectors can contain a set of pseudo-Goldstone mesons that exhibit a complicated structure in terms of stability and relative masses. Stable ones can act as dark matter candidates, while their interactions with the unstable ones determine their relic abundances. The overall structure, by specifying which channels are kinematically forbidden or not, affects the cosmology, constraints and collider phenomenology. In this paper, we present a classification of these pseudo-Goldstone meson structures. We find that the structures can be classified into three categories, corresponding to strong, suppressed and essentially non-existent constraints from indirect detection. Limits on decay lengths of the unstable mesons and dark jet properties are presented for several benchmark models.