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 that are suppressed by a special sum rule. All couplings are suppressed by an undetermined UV scale, which needs to exceed 10$^{12}$ 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.