High quality axion in supersymmetric models

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)_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)TeV and F_a = $\mathcal{O}$(10¹⁵)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 ≠ 6, 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.