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

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 $\varphi$ 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 $\Delta \varphi =2\pi f_{\mathrm{eff}}\sim e^{\xi N}f$ for $\xi =\mathcal{O}(1)$, both the scalar potential driving the evolution of $\varphi$ during the inflationary epoch and the $\varphi$-dependent Higgs boson mass vary with an exponentially large periodicity of $\mathcal{O}(f_{\mathrm{eff}})$, while the back reaction potential stabilizing the relaxion has a periodicity of $\mathcal{O}(f)$. 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 $f\sim \sqrt{m_{\mathrm{SUSY}}{M}_{\ast }}$, where the soft SUSY breaking scalar mass $m_{\mathrm{SUSY}}$ can be well above the weak scale, and the fundamental scale $M_{\ast }$ can be identified as the Planck scale or the GUT scale.

Comments: 20 pages, 2 figures; v2: a reference and related comment added