A see-saw scenario of an $A_4$ flavour symmetric standard model

A see-saw scenario for an $A_4$ flavour symmetric standard model is presented. As before, the see-saw mechanism can be realized in several models of different types depending on different ways of neutrino mass generation corresponding to the introduction of new fields with different symmetry structures. In the present paper, a general desription of all these see-saw types is made with a more detailed investigation on type-I models. As within the original see-saw mechanism, the symmetry structure of the standard model fields decides the number and the symmetry structure of the new fields. In a model considered here, the scalar sector consists of three standard-model-Higgs-like iso-doublets ($SU_L(2)$-doublets) forming an $A_4$ triplet. The latter is a superposition of three mass-eigen states, one of which could be identified with the recently discovered Higgs boson. A possible relation to the still-deliberated 750 GeV diphoton resonance at the 13 TeV LHC collisions is also discussed. In the lepton sector, the three left-handed lepton iso-doublets form an $A_4$-triplet, while the three right-handed charged leptons are either $A_4$-singlets $(1,1',1'')$ in one version of the model, or components of an $A_4$-triplet in another version. To generate neutrino masses through the type-I see-saw mechanism it is natural to add four right-handed neutrino multiplets, including one $A_4$-triplet and three $A_4$-singlets $(1,1',1'')$. For an interpretation, the model is applied to deriving some physics quantities which can be compared with the experimental data. More precisely, the PMNS matrix obtained after fitting with the current experimental data is checked by being used to calculating several quantities, such as neutrinoless double beta decay effective mass $|\langle m_{ee}\rangle|$, CP violation phase $\delta_{CP}$ and Jarlskog parameter $J_{CP}$, which can be verified experimentally.