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.

Figure 1

The white region shows the allowed parameter space of the Nelson-Barr relaxion. The contours indicate the number of clockwork sites (black dashed), the relaxion-Higgs mixing (red dot-dashed), and the minimal dimension of the Planck-suppressed operators that should be forbidden (thin blue). The green-shaded region combines constraints from astrophysics [36, 37, 38, 39], extragalactic background light [5], and flavor-violating kaon decays [40]. The upper left grey region is ruled out by the bound in Eq. (8).

Figure 2

The white region shows the allowed parameter space of the Nelson-Barr relaxion. The different contour lines indicate the number of clockwork sites (black dashed), the relaxion-Higgs mixing (red dot-dashed), and the minimal dimension of the Planck-suppressed operators that should be forbidden (thin blue). The green-shaded region combines constraints from astrophysics [36, 37, 38, 39], extragalactic background light [5], and flavor-violating kaon decays [40].