Abstract
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 non-zero 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.
Highlights
The large hierarchy between the electroweak (EW) scale and the Planck scale, and the smallness of the strong CP phase compared to the Cabibbo-Kobayashi-Maskawa (CKM) phase are two of the main mysteries of modern particle physics
The main lesson of this work is that combining the relaxion mechanism with the NB construction leads to two positive outcomes: (i) the “relaxion CP problem,” induced by the Oð1Þ CP phase of the relaxion vacuum expectation value, is solved; (ii) the relaxion CP phase becomes the origin of the CKM phase
Our model serves as an existence proof of the NB relaxion setup, focusing on the simplest possible implementation, which captures some generic features of the construction
Summary
The large hierarchy between the electroweak (EW) scale and the Planck scale, and the smallness of the strong CP phase compared to the Cabibbo-Kobayashi-Maskawa (CKM) phase are two of the main mysteries of modern particle physics. The relaxion is the pseudo-NambuGoldstone boson of a spontaneously broken Abelian symmetry Uð1Þclock that gets explicitly broken by two sequestered sectors with exponentially hierarchical charges These sectors feed into the relaxion potential, generating exponentially different periodicities. The structure of the relaxion potential forces it to get a vacuum expectation value (VEV), introducing a CPviolating phase in the theory [1,5] At the end of this paper, we discuss how the spontaneous breaking of Uð1Þclock at a high scale poses a “relaxion quality problem,” which is related to the theoretical challenge of screening Planck-suppressed effects in order to preserve the peculiar structure of the relaxion potential
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