Neutrino Mass Hierarchy and Axion--Lepton Couplings in a Minimal Flavored $ν$KSVZ Model

By treating the PQ symmetry as a flavor symmetry, we construct a minimal flavored axion model by combining the KSVZ axion framework with the type-I seesaw mechanism. This minimal setup introduces flavor-dependent PQ charge assignments and two additional SM singlet scalar fields, leading to a specific zero texture in the inverse Majorana neutrino mass matrix. This texture, together with the observed smallness of $θ_{13}$, predicts an approximate inverted GST-like relation, implying an inverted neutrino mass ordering with $17\lesssim m_1/m_3\lesssim45$. Assuming no strong hierarchy among the relevant Majorana Yukawa couplings, this ordering is naturally determined by the ratio of the vacuum expectation values of the two SM-singlet scalar fields. This predicted inverted structure is the most readily testable feature of our model, given that current experiments favor the normal ordering. Nevertheless, since the inverted one has not been ruled out, a viable parameter space still remains. We also perform a comprehensive study of the axion--lepton interactions in this framework. The induced axion--neutrino couplings satisfy current astrophysical constraints while potentially affecting neutrino oscillations under suitable conditions. Furthermore, we derive analytical expressions for the axion couplings to charged leptons by evaluating the one-loop radiative corrections in a largely model independent framework and assess the corresponding experimental constraints.