We present an $A4$-based model where neutrino masses arise from a combination of seesaw mechanisms. The model is motivated by several small mixing and mass parameters indicated by the data. These are ${\theta }_{13}$, the solar mass splitting, and the small deviation of ${\theta }_{23}$ from maximal mixing ($=\pi /4$). We take the above as indications that at some level the small quantities are well approximated by zero. In particular, the mixing angles to zeroth order should be either 0 or $\pi /4$. Accordingly, in this model the type-II seesaw dominates and generates the larger atmospheric mass splitting and sets ${\theta }_{23}=\pi /4$. The other mixing angles are vanishing as is the solar splitting. We show how the $A4$ assignment for the lepton doublets leads to this form. We also specify the $A4$ properties of the right-handed neutrinos which result in a smaller type-I seesaw contribution that acts as a perturbation and shifts the angles ${\theta }_{12}$ and ${\theta }_{13}$ into the correct range and the desired value of $\mathrm{\Delta }{m}_{\text{solar}}^2$ is produced. The $A4$ symmetry results in relationships between these quantities as well as with a small deviation of ${\theta }_{23}$ from $\pi /4$. If the right-handed neutrino mass matrix $M_R$ is chosen real then there is no leptonic $CP$ violation and only normal ordering is admissible. If $M_R$ is complex then inverted ordering is also allowed with the proviso that the $CP$ phase $\delta$ is large, i.e., $\sim \pi /2$ or $-\pi /2$. The preliminary results from $\mathrm{NO}\nu \mathrm{A}$ favoring normal ordering and $\delta$ near $-\pi /2$ imply quasidegenerate neutrino masses in this model.

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• Neutrinos
• Sterile neutrinos