Leptons and Quarks from a Discrete Flavor Symmetry

We propose a new model of leptons and quarks based on the discrete flavor symmetry $T'$, the double covering of $A_4$, in which the hierarchies of charged fermion masses and the mildness of neutrino masses are responsible for Higgs scalars. After spontaneous breaking of flavor symmetry, with the constraint of renormalizability in the Lagrangian, the leptons have $m_{e}=0$ and the quarks have the Cabibbo-Kobayashi-Maskawa (CKM) mixing angles $\theta^{q}_{12}=13^{\circ}, \theta^{q}_{23}=0^{\circ}$ and $\theta^{q}_{13}=0^{\circ}$. Thus, certain effective dimension-5 operators are introduced, which induce $m_{e}\neq0$ and lead the quark mixing matrix to the CKM one in form. On the other hand, the neutrino Lagrangian still keeps renormalizability. For completeness, we show numerical analysis: in the lepton sector, only normal mass hierarchy is permitted within $3\sigma$ experimental bounds with the prediction of both large deviations from maximality in the atmospheric mixing angle $\theta_{23}$ and the measured values of reactor angle. So, future precise measurements of $\theta_{23}$, whether $\theta_{23}\rightarrow45^{\circ}$ or $|\theta_{23}-45^{\circ}|\rightarrow5^{\circ}$, will either exclude or favor our model. Together with it, our model makes predictions for the Dirac CP phase, which is almost compatible with the global analysis in $1\sigma$ experimental bounds. Moreover, we show the effective mass $|m_{ee}|$ measurable in neutrinoless double beta decay to be in the range $0.04\lesssim|m_{ee}|[eV]<0.11$, which can be tested in near future neutrino experiments.