Spontaneous CP violation, sterile neutrino dark matter and leptogenesis

We constructed a model for spontaneous CP symmetry breaking in five-dimensional space-time that has a potential to solve the strong CP problem. To explain the nature of dark matter and the baryon asymmetry of the universe, three right-handed neutrinos and $U{\left(1\right)}_{B-L}$ gauge interaction are introduced in the bulk, in addition to the field contents of the Bento-Branco-Parada model. The wave-function profiles in the fifth dimension can suppress dangerous operators allowed by symmetries, and the scale of spontaneous CP symmetry breaking can be sufficiently large to be consistent with thermal leptogenesis. In this model, the lightest right-handed neutrino serves as dark matter with a mass of $O\left(10\right)$ keV. This small mass and the necessarily small mixing are explained by the exponentially localized wave-function in the fifth dimension due to a bulk mass term. The correct relic abundance is achieved thanks to the $U{\left(1\right)}_{B-L}$ gauge interaction. The other heavy right-handed neutrinos explain the baryon asymmetry of the universe through leptogenesis, with the required CP violating phases generated by interactions involving heavy leptons.