Flavonic dark matter

We first time show that a common solution to dark matter and the flavor problem of the standard model can be obtained in the framework of the $\mathcal{Z}_{\rm N} \times \mathcal{Z}_{\rm M}$ flavor symmetry where the flavonic Goldstone boson of this flavor symmetry acts as a good dark matter candidate through the misalignment mechanism. Hierarchical mass pattern of quarks and charged leptons naturally follows from the discrete symmetry. For light active neutrinos, we construct the Dirac-type mass matrix which is preferred to fit the observed neutrino oscillation data with normal hierarchy. Our model predicts the axion-like photon coupling characteristically different from the standard QCD axion, and could be probed by the future X-ray or radio observations.