Is the Relaxion an Axion?

TL;DR

This paper critically examines the relaxion mechanism, arguing it breaks gauge symmetry and suggesting the cutoff scale is limited near the electroweak scale, with potential ways to extend it to address the little hierarchy problem.

Contribution

It demonstrates that the simplest relaxion models break gauge symmetry, challenging their naturalness and cutoff scale, and explores models with familons to potentially extend the cutoff and address collider and dark matter issues.

Findings

The relaxion mechanism breaks gauge symmetry, affecting its naturalness.

The cutoff scale in simple models is near the electroweak scale.

A familon-based model can potentially raise the cutoff and provide dark matter candidates.

Abstract

We consider the recently proposed cosmological relaxation mechanism where the hierarchy problem is ameliorated, and the electroweak scale is dynamically selected by a slowly rolling axion field. We argue that, in its simplest form, the construction breaks a gauge symmetry that always exists for pseudo-Nambu-Goldstone bosons (in particular the axion). The small parameter in the relaxion model is therefore not technically natural as it breaks a gauge symmetry rather than global symmetries only. The consistency of the theory generically implies that the cutoff must lie around the electroweak scale, but not qualitatively higher. We discuss several ways to evade the above conclusion. Some of them may be sufficient to increase the cutoff to the few-TeV range (and therefore may be relevant for the little-hierarchy problem). To demonstrate the ideas in a concrete setting we consider a model with a familon, the Nambu-Goldstone boson of a spontaneously broken chiral flavor symmetry. The model has some interesting collider-physics aspects and contains a viable weakly interacting dark matter candidate.