Nelson-Barr relaxion

Cosmological relaxation models in which the relaxion is identified with the QCD axion, generically fail to account for the smallness of the strong CP phase. We present a simple alternative solution to this "relaxion CP problem" based on the Nelson-Barr mechanism. We take CP to be a symmetry of the UV theory, and the relaxion to have no anomalous coupling with QCD. The nonzero vacuum expectation value of the relaxion breaks CP spontaneously, and the resulting phase is mapped to the Cabibbo-Kobayashi-Maskawa phase of the Standard Model. The extended Nelson-Barr quark sector generates the relaxion "rolling" potential radiatively, relating the new physics scale with the relaxion decay constant. With no new states within the reach of the LHC, our relaxion can still be probed in a variety of astrophysical and cosmological processes, as well as in flavor experiments.