The Hierarchion, a Relaxion Addressing the Standard Model's Hierarchies

TL;DR

The paper introduces the hierarchion, a relaxion mechanism that simultaneously addresses the electroweak, strong CP, and flavor hierarchies of the Standard Model, linking them through a unified symmetry-based framework.

Contribution

It proposes a novel relaxion model that unifies solutions to multiple Standard Model hierarchies using a single pseudo-Nambu-Goldstone boson linked to flavor and CP symmetries.

Findings

The hierarchion can naturally generate the electroweak scale and flavor textures.

The model explains neutrino masses and mixings without extra electroweak states.

Potential experimental signatures include flavor-violating decays of leptons and mesons.

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. An 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 construction is the relaxion, which we call the hierarchion because it is essentially linked to our construct 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.