Topological Freeze-out by Semi-Annihilation

We point out that a QCD-like dark sector can be coupled to the Standard Model by gauging the topological Skyrme current, which measures the dark baryon number in the infrared, to give a technically natural model for dark matter. This coupling allows for a semi-annihilation process $\chi \chi \rightarrow \chi X_\mu$, where $X_\mu$ is the gauge boson mediator and $\chi$ a dark pion field, which plays the dominant role in setting the dark matter relic abundance. The topological interaction is purely $p$-wave and so free from indirect detection constraints. We show that the dark matter pion mass needs to be in the range $10$ MeV $\lesssim m_\chi \lesssim$ $1$ TeV; towards the lighter end of this range, there can moreover be significant self-interactions. We discuss prospects for probing this scenario at collider experiments, ranging from the LHC to low-energy $e^+ e^-$ colliders, future Higgs factories, and beam-dump experiments.