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

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 ≫ 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 eff ∼ e ξN f for ξ = 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 O(feff) , while the back reaction potential stabilizing the relaxion has a periodicity of 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~ √mSUSYM , where the soft SUSY breaking scalar mass m SUSY can be well above the weak scale, and the fundamental scale M * can be identified as the Planck scale or the GUT scale.