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We propose a quark and lepton model explaining their masses, mixings, and CPviolating phases, introducing modular $A_4$ and hidden gauged $U(1)$symmetries. The hidden $U(1)$ brings us heavier Majorana fermions that arerequested by chiral anomaly cancellations, and we work on a canonical seesawscenario due to their neutral particles.In this framework, we search forfavorite parameter space to satisfy both the experimental values and showpredictions, applying the $\chi$ square analysis.Then, we discuss a bosonicdark matter candidate that only annihilates into muon state due to the modular$A_4$ flavor symmetry where we suppose the main interaction of dark matter tobe Yukawa terms. And we study muon anomalous magnetic dipole moment where thereare not any constraints of lepton flavor violations thanks to this flavorsymmetry. Finally, we show the allowed space to satisfy the observed relicdensity of dark matter and the muon anomalous magnetic dipole moment.

Quark and lepton model with flavor specific dark matter and muon $g-2$ in modular $A_4$ and hidden $U(1)$ symmetries