# Axion Misalignment Driven to the Hilltop

## TL;DR

This paper proposes a dynamical mechanism in supersymmetric models that naturally sets the axion misalignment angle near the hilltop, explaining the fine-tuning and predicting specific axion decay constants with no isocurvature perturbations.

## Contribution

It introduces a model where the axion dynamically relaxes to the hilltop, providing a natural explanation for the initial condition required for low decay constants.

## Key findings

- Predicts axion decay constant in the range 3×10^9 to 10^10 GeV.
- Demonstrates no isocurvature perturbations in the model.
- Provides explicit supersymmetric examples with natural Higgs-inflaton couplings.

## Abstract

The QCD axion serves as a well-motivated dark matter candidate and the misalignment mechanism is known to reproduce the observed abundance with a decay constant $f_a \simeq \mathcal{O}(10^{12})$ GeV for a misalignment angle $\theta_{\rm mis} \simeq \mathcal{O}(1)$. While $f_a \ll 10^{12}$ GeV is of great experimental interest, the misalignment mechanism requires the axion to be very close to the hilltop, i.e. $\theta_{\rm mis} \simeq \pi$. This particular choice of $\theta_{\rm mis}$ has been understood as fine-tuning the initial condition. We offer a dynamical explanation for $\theta_{\rm mis} \simeq \pi$ in a class of models. The axion dynamically relaxes to the minimum of the potential by virtue of an enhanced mass in the early universe. This minimum is subsequently converted to a hilltop because the CP phase of the theory shifts by $\pi$ when one contribution becomes subdominant to another with an opposite sign. We demonstrate explicit and viable examples in supersymmetric models where the higher dimensional Higgs coupling with the inflaton naturally achieves both criteria. Associated phenomenology includes a strikingly sharp prediction of $3 \times 10^9$ GeV $\lesssim f_a \lesssim 10^{10}$ GeV and the absence of isocurvature perturbation.