Muon $g-2$ and neutrino mass explanations in a modular $A_4$ symmetry

We construct a successful model to explain the muon anomalous magnetic moment originated from Yukawa terms. Thanks to a modular $A_4$ flavor symmetry, there are not any lepton flavor violations from the terms that would spoil the model. We also investigate a predictive radiative seesaw model including dark matter candidate at favorable fixed points of $\tau=\omega,\ i$ obtained by recent analysis of the stabilized moduli values from the possible configurations of the flux compactifications. In the result, we show our predictions on the Dirac CP and Majorana phases, the neutrino masses through $\chi^2$ analysis. Then, we demonstrate the allowed regions to satisfy the muon anomalous magnetic moment and the observed relic density of dark matter in terms of valid mass eigenstates.
Comment: 28 pages, 14 figures, we updated new figures and added some discussions on neutrino mass explanations