Inverted mass hierarchy from a flavored axion-neutrino model

Combining the KSVZ axion model and the type-I seesaw mechanism, we construct a minimal flavored axion model that can affect the neutrino mass matrix. This minimal model requires a flavor dependent PQ charge assignment and two additional standard model (SM) singlet scalars which generate specific patterns of lepton mass matrices, yielding a particular texture of Majorana neutrino mass matrix. Combined with fact that $\theta _{13}$ is much smaller than the other mixing angles, this texture predicts an Inverted Hierarchy of neutrino masses with $17\lesssim m_1/m_3\lesssim 44$, and a hierarchy between the two VEVs of SM-singlet scalars. We also examine the couplings between the axion and the leptons in this model. Especially, the axion-neutrino couplings have the potential effect on neutrino oscillation.