Abstract
We present a mechanism that addresses the electroweak, the strong CP, and the flavor hierarchies of the Standard Model (including neutrino masses) in a unified way. The naturalness of the electroweak scale is solved together with the strong CP problem by the Nelson-Barr relaxion: the relaxion field is identified with the pseudo-Nambu-Goldstone boson of an abelian symmetry with no QCD anomaly. The Nelson-Barr sector generates the “rolling” potential and the relaxion vacuum expectation value at the stopping point is mapped to the Cabibbo-Kobayashi-Maskawa phase. The same abelian symmetry accounts for the Standard Model’s mass hierarchies and flavor textures through the Froggatt-Nielsen mechanism. We show how the “backreaction” potential of the relaxion can be induced by a sterile neutrino sector, without any extra state with electroweak quantum numbers. The same construction successfully explains neutrino masses and mixings. The only light field in our model is the relaxion, which we call the hierarchion because it is central to our construction that accounts for all the Standard Model hierarchies. Given its interplay with flavor symmetries, the hierarchion can be probed in flavor-violating decays of the Standard Model fermions, motivating a further experimental effort in looking for new physics in rare decays of leptons and mesons.
Highlights
The “rolling” sector and the “backreaction” sector
We present a mechanism that addresses the electroweak, the strong CP, and the flavor hierarchies of the Standard Model in a unified way
Since the Z2 symmetry is spontaneously broken by the vacuum expectation value (VEV) of ΦN, threshold corrections induced by higher dimensional operators like ΦN QHψuc and ΦN QHψdc can spoil the above structure, and need to be small enough to satisfy the upper bound on the strong CP phase
Summary
We give a brief review of the relaxion [1] and the clockwork [3,4,5] mechanisms to set up our notation. The U(1)clock gets broken explicitly by two sectors that are sequestered from each other: the rolling sector and the backreaction sector Each of these explicit breaking sources induces a potential for the relaxion field with periodicity proportional to the relaxion decay constant divided by the charges carried by the fields in each sector. One way to create such a hierarchy of charges is the so-called clockwork mechanism [3,4,5] This construction introduces N + 1 spontaneously broken abelian symmetries at different sites of a moose diagram, as shown in figure 1.2 The potential is Vclock =. As we discuss, the backreaction potential can be generated by a 10 GeV scale sterile neutrino sector that breaks U(1)clock at the first site of the clockwork chain
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