Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry

TL;DR

This paper proposes a model using multiple axions to implement the relaxion solution to the hierarchy problem, with a UV completion in high-scale supersymmetry that naturally generates the necessary axion scales.

Contribution

It introduces a multi-axion relaxion model with an exponentially long flat direction and provides a UV completion within high-scale supersymmetry frameworks.

Findings

The relaxion field corresponds to an exponentially long multi-helical flat direction.

The model achieves large periodicities in the scalar potential and Higgs mass variation.

A natural UV completion is realized in high-scale or split supersymmetry scenarios.

Abstract

We discuss a scheme to implement the relaxion solution to the hierarchy problem with multiple axions, and present a UV-completed model realizing the scheme. All of the $N$ axions in our model are periodic with a similar decay constant $f$ well below the Planck scale. In the limit $N\gg 1$, the relaxion $\phi$ corresponds to an exponentially long multi-helical flat direction which is shaped by a series of mass mixing between nearby axions in the compact field space of $N$ axions. With the length of flat direction given by $\Delta \phi =2\pi f_{\rm eff} \sim e^{\xi N} f$ for $\xi={\cal O}(1)$, both the scalar potential driving the evolution of $\phi$ during the inflationary epoch and the $\phi$-dependent Higgs boson mass vary with an exponentially large periodicity of ${\cal O}(f_{\rm eff})$, while the back reaction potential stabilizing the relaxion has a periodicity of ${\cal O}( f)$. A natural UV completion of our scheme can be found in high scale or (mini) split supersymmetry (SUSY) scenario with the axion scales generated by SUSY breaking as $f\sim \sqrt{m_{\rm SUSY}M_*}$, where the soft SUSY breaking scalar mass $m_{\rm SUSY}$ can be well above the weak scale, and the fundamental scale $M_*$ can be identified as the Planck scale or the GUT scale.