All-in-one Relaxion, a unified solution to five BSM puzzles

We present a unified relaxion solution to the five major outstanding issues in particle physics: the hierarchy problem, 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 vector-like 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, $\partial_\mu \phi J^\mu$, 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 ${\cal O}(1)$ strong CKM phase is generated, the induced strong CP phase is much smaller, i.e., within experimental bounds.