We present a unified relaxion solution to the five major outstanding issues in particle physics: Higgs mass naturalness, dark matter, matter-antimatter asymmetry, neutrino masses and the strong $CP$ problem. The only additional field content in our construction with respect to standard relaxion models is an up-type vectorlike fermion pair and three right-handed neutrinos charged under the relaxion shift symmetry. The observed dark matter abundance is generated automatically by oscillations of the relaxion field that begin once it is misaligned from its original stopping point after reheating. The matter-antimatter asymmetry arises from spontaneous baryogenesis induced by the $CPT$ violation due to the rolling of the relaxion after reheating. The $CPT$ violation is communicated to the baryons and leptons via an operator, ${\partial }_{\mu }\varphi J^{\mu }$, where $J^{\mu }$ consists of right-handed neutrino currents arising naturally from a simple neutrino mass model. Finally, the strong $CP$ problem is solved via the Nelson-Barr mechanism, i.e., by imposing $CP$ as a symmetry of the Lagrangian that is broken only spontaneously by the relaxion. The $CP$ breaking is such that although an $\mathcal{O}(1)$ strong Cabibbo-Kobayashi-Maskawa (CKM) phase is generated, the induced strong $CP$ phase is much smaller, i.e., within experimental bounds.

• Received 24 May 2019

DOI:https://doi.org/10.1103/PhysRevD.100.055003

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Published by the American Physical Society