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 ∆φ = 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(f eff ), 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 ∼ √ m SUSY M * , 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.

We discuss the effective interactions of axion supermultiplet, which might be important for analyzing the cosmological aspect of supersymmetric axion model. Related to axino cosmology, it is stressed that three seemingly similar but basically different quantities, the Wilsonian axino-gluino-gluon coupling, the 1PI axino-gluino-gluon amplitude, and the PQ anomaly coefficient, should be carefully distinguished from each other for correct analysis of the thermal production of axinos in the early Universe. It is then noticed that the 1PI axino-gluino-gluon amplitude at energy scale p in the range M Φ < p < v P Q is suppressed by M 2 Φ /p 2 in addition to the well-known suppression by p/16π 2 v P Q , where M Φ is the mass of the heaviest PQ-charged and gauge-charged matter supermultiplet in the model, which can be well below the PQ scale v P Q . As a result, axino production at temperature T > M Φ is dominated by the production by matter supermultiplet, not by the production by gauge supermultiplet. Still the axino production rate is greatly reduced if M Φ ≪ v P Q , which would make the subsequent cosmology significantly altered. This would be most notable in the supersymmetric DFSZ model in which M Φ corresponds to the Higgsino mass which is around the weak scale, however a similar reduction is possible in the KSVZ model also. We evaluate the relic axino density for both the DFSZ and KSVZ models while including the axino production in the processes involving the heaviest PQ-charged and gauge-charged matter supermultiplet.

We examine the low energy phenomenology of the relaxion solution to the weak scale hierarchy problem. Assuming that the Hubble friction is responsible for a dissipation of the relaxion energy, we identify the cosmological relaxion window which corresponds to the parameter region compatible with a given value of the acceptable number of inflationary e-foldings. We then discuss a variety of observational constraints on the relaxion window, including those from astrophysical and cosmological considerations. We find that majority of the parameter space with a relaxion mass m φ 100 eV or a relaxion decay constant f 10 7 GeV is excluded by existing constraints. There is an interesting parameter region with m φ ∼ 0.2 − 10 GeV and f ∼ few − 200 TeV, which is allowed by existing constraints, but can be probed soon by future beam dump experiments such as the SHiP experiment, or by improved EDM experiments.

We revisit the flavor-changing processes involving an axion-like particle (ALP) in the context of generic ALP effective lagrangian with a discussion of possible UV completions providing the origin of the relevant bare ALP couplings. We focus on the minimal scenario that ALP has flavor-conserving couplings at tree level, and the leading flavor-changing couplings arise from the loops involving the Yukawa couplings of the Standard Model fermions. We note that such radiatively generated flavor-changing ALP couplings can be easily suppressed in field theoretic ALP models with sensible UV completion. We discuss also the implication of our result for string theoretic ALP originating from higher-dimensional p-form gauge fields, for instance for ALP in large volume string compactification scenario. *

We study the cosmological impact of the supersymmetric DFSZ axion model. Extending recent works, we first provide a comprehensive analysis of thermal production of the DFSZ axino considering all the possible scattering, decay and inverse decay processes depending on various mass parameters and the reheat temperature. Although it is hard for the DFSZ axino to be in thermal equilibrium, its coupling is still large enough to generate huge axino population which can turn into overabundant neutralino density. We examine the neutralino parameter space to identify the dark matter property depending on the Peccei-Quinn scale. As the Peccei-Quinn scale becomes higher resulting in longer axino lifetime, the neutralino dark matter appears in a lighter Higgsino-like LSP region or a more restricted Bino-like LSP region allowing a resonant annihilation through a CP-odd Higgs boson to meet stronger reannihilation.