  QCD-like theories in which the dark matter (DM) of the Universe is
hypothesized to be a thermal relic in the form of a dark pion has been
extensively investigated, with most studies neglecting the CP-violating
$\theta$-angle associated with the topological vacuum. We point out that a
non-vanishing $\theta$ could potentially trigger resonant number-changing
processes giving rise to the observed relic density in agreement with
perturbative unitarity as well as observations of clusters of galaxies. This
constitutes a novel production mechanism of MeV DM and an alternative to those
relying on the Wess-Zumino-Witten term. Moreover, for specific meson mass
spectra, similar resonant scatterings serve as a realization of
velocity-dependent self-interacting DM without a light mediator. Explicit
benchmark models are presented together with a discussion of possible signals,
including gravitational waves from the chiral phase transition associated with
the dark pions.
