Is the Relaxion an Axion?

TL;DR

The paper questions whether the cosmological relaxation mechanism can be realized with a pNGB such as an axion, showing that the required small coupling breaks a gauge symmetry and generically forces the EFT cutoff $\Lambda$ to lie near the electroweak scale. It demonstrates a general no-go relation that constrains $\Lambda$ unless additional structure or non-compact field realizations are introduced, and discusses several proposed evasion strategies. To make the discussion concrete, it constructs a calculable familon model in which the backreaction and radiative corrections can be analyzed explicitly, finding that the cutoff remains at the TeV scale under reasonable assumptions. The work also identifies a weakly interacting dark matter candidate and distinctive collider signatures, highlighting that pushing the cutoff well above the TeV scale within a pNGB relaxion framework remains challenging without new UV ingredients.

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.

Figures (1)

• Figure 1: Constraints from dark matter phenomenology on our parameter space. We define $y_1=y \cos \theta$, $y_2=y \sin \theta$ , and fix $\tan \theta = -2$. The parameter $m_L$ is adjusted at each point to match the observed relic density. The region shaded in grey is excluded by LUX, while the brown region will be probed in the near future by the XENON 1 Ton experiment. The blue lines correspond to the following cutoffs: the one saturating the cosmological constraints of Eq. \ref{['eq:cutoff']} with $f= \frac{f_{\rm UV}}{2 n} = 10$ TeV (dot-dashed), the one from Eq. \ref{['derivnew']} with $f_{\rm UV} = M_{{\rm Pl}}$, so that the field excursion remains sub-Planckian, and $f= 10$ TeV (dashed), and the one from Eq. \ref{['derivnew']} with $n=10$ (solid).