CPon Dark Matter

We study a class of supersymmetric models where the strong CP problem is solved through spontaneous CP violation, carried out by a complex scalar field that determines the Yukawa couplings of the theory. Assuming that one real component of this field - the CPon - is light, we examine the conditions under which it provides a viable Dark Matter candidate. The CPon couplings to fermions are largely determined by the field-dependent Yukawa interactions, and induce couplings to gauge bosons at 1-loop. All couplings are suppressed by an undetermined UV scale, which needs to exceed 1012 GeV in order to satisfy constraints on excessive stellar cooling and rare kaon decays. The CPon mass is limited from below by 5th force experiments and from above by X-ray telescopes looking for CPon decays to photons, leaving a range roughly between 10 meV and 1 MeV. Everywhere in the allowed parameter space the CPon can saturate the observed Dark Matter abundance through an appropriate balance of misalignment and freeze-in production from heavy SM fermions.