Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry (1511.00132v2)

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.

• The paper introduces a multi-axion relaxion model that employs a helicoidal structure to exponentially enhance the effective field range for addressing the hierarchy problem.
• It demonstrates how sub-Planckian decay constants and strategic mass mixings facilitate a dynamic scanning and stabilization of the Higgs mass during inflation.
• The study shows that embedding the model in a high-scale or mini split SUSY framework provides a natural UV completion that protects against radiative corrections.

Overview of Multi-Axion Relaxion Framework and UV Completion with Supersymmetry

The paper by Kiwoon Choi and Sang Hui Im presents a sophisticated model addressing the hierarchy problem through the use of the relaxion mechanism facilitated by multiple axions. This approach is augmented by a unique ultraviolet (UV) completion framework involving high-scale or mini split supersymmetry (SUSY).

The relaxion idea involves a scalar field that dynamically adjusts the Higgs boson mass during the inflationary period, thereby tackling the hierarchy problem without fine-tuning assumptions. The mechanism requires a stark contrast between two scale parameters in the field potential: (1) a long excursion range required for the scanning of the Higgs mass and (2) a smaller scale related to the periodic nature of the stabilizing potential. This model introduces $N$ axions, each with a decay constant that is sub-Planckian, and relies on a creative helicoidal structure for these axions to produce the required large excursion range.

Model Specification

In the model, the relaxion field $\phi$ is realized as part of a multi-axion system, characterized by a long helical structure in the compact field space formed by $N$ axions with similar decay constants $f < M_{\text{Planck}}$. In the limit where $N \gg 1$, this structure achieves a large effective field range, specifically, $$\Delta \phi = 2\pi f_{\text{eff}} \approx e^{\xi N} f$$ where $\xi = \mathcal{O}(1)$. This is accomplished through a series of mass mixings between adjacent axions, resulting in the necessary field excursion length to resolve the hierarchy issue without introducing unrealistic assumptions.

UV Completion and Supersymmetry

The authors propose that a natural UV completion for this multi-axion relaxion model can be achieved within a high-scale or mini split SUSY framework. In this context, SUSY breaking scales generate the necessary axion decay constants in the form $f \sim \sqrt{m_{\rm SUSY} M_*}$. Here, $m_{\rm SUSY}$ represents a soft SUSY-breaking scalar mass that lies above the electroweak scale, whereas $M_*$ denotes a fundamental scale that can be equivalently matched to the GUT or Planck scale.

This setup supports the robustness of the model against radiative corrections. The axion-induced potential is described as having periodic structures with large periodicities, primarily determined through back-reactions stabilized at smaller scales aligning the Higgs vacuum expectation value to be consistent with the observed weak scale.

Implications and Future Directions

This work implies significant avenues for alternate explorations of the hierarchy problem, particularly focusing on the interplay between axion physics and high-energy scale symmetry structures. The exponential alignment mechanism introduced could pioneer new investigations into how multiple axion fields can be harmonized within other theoretical frameworks.

The paper explicitly shows the feasibility of achieving naturally small electroweak scales, thereby providing a compelling alternate pathway to resolving long-standing issues in theoretical particle physics without heavy reliance on non-compact field ranges or additional fine-tuning. It showcases a remarkable blend of concepts from cosmology, supersymmetric models, and axion physics, thus potentially influencing future theoretical and experimental pursuits aimed at exploring the fundamental parameters of our universe.

Building on this framework could involve further probing into the potential landscape of SUSY models and examining experimental signatures that such a multi-axion relaxion framework might manifest.

In conclusion, Choi and Im’s research remarks a valuable contribution to the innovative use of the relaxion mechanism leveraged with axion dynamics, augmented by high-scale SUSY, pointing to a nuanced pathway for addressing prevalent issues related to the hierarchy problem.