Dark matter in QCD-like theories with a theta vacuum: Cosmological and astrophysical implications

Quantum chromodynamics (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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math>-violating <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>θ</c:mi></c:mrow></c:math>-angle associated with the topological vacuum. We point out that a nonvanishing <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>θ</e:mi></e:math> 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.