Naturalness of the relaxion mechanism

TL;DR

This paper uses Bayesian statistics to evaluate the plausibility of relaxion models as solutions to the hierarchy problem, finding that standard cosmology favors the Standard Model over relaxion scenarios due to fine-tuning issues.

Contribution

First statistical analysis quantifying the plausibility of relaxion models versus the Standard Model using Bayesian methods and cosmological constraints.

Findings

Relaxion models are generally favored by large Bayes-factors without cosmological constraints.

Constraints on vacuum energy and QCD θ-term reduce relaxion plausibility.

Including inflationary bounds strongly favors the Standard Model over relaxion models.

Abstract

The relaxion mechanism is a novel solution to the hierarchy problem. In this first statistical analysis of the relaxion mechanism, we quantify the relative plausibility of a QCD and a non-QCD relaxion model versus the Standard Model with Bayesian statistics, which includes an automatic penalty for fine-tuning. We find that in light of the hierarchy between the weak and Planck scales, relaxion models are favoured by colossal Bayes-factors. Constraints upon \eg the vacuum energy during relaxation, however, shrink the Bayes-factors such that relaxion models are only slightly favoured. Including the bounds on $\left|\theta_\text{QCD}\right|$ shatters the plausibility of the QCD relaxion model as it typically yields $\left|\theta_\text{QCD}\right| \gg 0$. Finally, we augment our models with scalar-field inflation and consider measurements of inflationary observables from BICEP/Planck. We find that, all told, the Standard Model is favoured by huge Bayes-factors as the relaxion models require fine-tuning such that the Hubble parameter is less than the height of the periodic barriers. Thus, whilst we confirm that relaxion models could solve the hierarchy problem, we find that their unconventional cosmology demolishes their plausibility.