High Quality Axion in Supersymmetric Models

TL;DR

This paper demonstrates how well-motivated symmetries in supersymmetric models can naturally ensure high-quality axions, addressing the axion quality problem without introducing ad hoc symmetries, and remains valid for large gravitino masses and decay constants.

Contribution

It shows that combining supersymmetry, $U(1)_{B-L}$, and discrete R-symmetry $Z_{NR}$ guarantees high-quality axions, resolving the axion quality problem through anomaly cancellation and symmetry interplay.

Findings

The interplay of symmetries guarantees axion quality for large $m_{3/2}$ and $F_a$.

Introduction of new matter fields cancels anomalies, supporting large $Z_{NR}$ symmetry.

The mechanism effectively equates $Z_{NR}$ to $U(1)_R$, solving the axion quality issue.

Abstract

In this work, we discuss how the use of the symmetries well motivated in physics beyond the Standard model (BSM) can guarantee the high quality axions. We avoid to introduce symmetries only useful for addressing the axion quality problem. Rather, we rely on symmetries well motivated by other issues in BSM: supersymmetry, $U(1)_{\rm B-L}$ and the discrete R-symmetry $Z_{NR}$. We show that the interplay among these guarantees the high quality of the axion even for the gravitino mass and axion decay constant as large as $m_{3/2}=\mathcal{O}(10){\rm TeV}$ and $F_{a}=\mathcal{O}(10^{15}){\rm GeV}$ respectively. The key point of this work relies on the observation that the MSSM contribution to the mixed anomalies $Z_{NR}-[SU(2)_{L}]^{2}$ and $Z_{NR}-[SU(3)_{c}]^{2}$ is not enough for gauging $Z_{NR}$ for $N\neq6$, which necessitates the introduction of new matter fields. We make the introduction to achieve zero mixed anomalies, which logically supports a desired large enough $N$ for $Z_{NR}$. This mechanism effectively makes $Z_{NR}$ equal to $U(1)_{R}$ and thus offers a logically complete solution to the axion quality problem.