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

TL;DR

The paper addresses the challenge of achieving a huge relaxion excursion by embedding the relaxion in a compact, multi-axion field space, where N axions with mass mixing produce an exponentially long flat direction with f_eff ≈ e^{ξN} f. This yields a large field range for the inflationary evolution and a separate, smaller back-reaction periodicity, enabling stabilization of the Higgs at a small VEV. A concrete UV completion in high-scale or mini-split SUSY generates the required axion decay constants and potentials, linking the relaxion dynamics to MSSM μ-problem solutions. The framework provides a technically natural mechanism for large-field relaxion dynamics and a consistent path to UV completion in SUSY theories.

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 $φ$ 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 $Δφ=2πf_{\rm eff} \sim e^{ξN} f$ for $ξ={\cal O}(1)$, both the scalar potential driving the evolution of $φ$ during the inflationary epoch and the $φ$-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.

Figures (2)

• Figure 1: Flat relaxion direction in the two axion model.
• Figure 2: Flat relaxion direction in the three axion case with $n_1=2$ and $n_2=4$.