High quality axion in supersymmetric models

Abstract

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 ZNR. 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 m3/2 = $$ \mathcal{O} $$ O (10)TeV and Fa = $$ \mathcal{O} $$ O (1015)GeV respectively. The key point of this work relies on the observation that the MSSM contribution to the mixed anomalies ZNR − [SU(2)L]2 and ZNR − [SU(3)c]2 is not enough for gauging ZNR 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 ZNR. This mechanism effectively makes ZNR equal to U(1)R and thus offers a logically complete solution to the axion quality problem.