Abstract
In a simple framework which naturally incorporates dark matter stability and neutrino phenomenology, we compute all the possible texture zeros which arise when the non-abelian flavor symmetry A4 is spontaneously broken to Z2. As a result, we obtain four textures with two vanishing matrix elements. Two of such textures predict a zero contribution to the neutrinoless double beta decay effective mass parameter at tree level, and as a one loop bound we get $m_{ee}<8\times 10^{-2}$ meV. These are compatible with the normal ordering for the neutrino masses and the allowed range for the lightest neutrino mass is between $m_{\nu_{min}}\sim3$ meV and $m_{\nu_{max}}\sim8$ meV. Additionally we obtain dark matter stability linked to the way the flavor symmetry is broken, leaving a residual Z2 symmetry
Highlights
The pattern of neutrino masses and mixing, which is very different from the quarks pattern, has been extensively studied
We demonstrate how some of the two-zero textures in the neutrino mass matrix can be obtained in a framework of the non-Abelian1 flavor symmetry A4
The texture zeros are related with the flavor symmetry breaking, the same that is responsible for the stability of dark matter (DM)
Summary
The pattern of neutrino masses and mixing, which is very different from the quarks pattern, has been extensively studied. We demonstrate how some of the two-zero textures in the neutrino mass matrix can be obtained in a framework of the non-Abelian flavor symmetry A4. In this framework, the dark matter (DM) stability is due to a residual Z2 symmetry of A4. In this model, the texture zeros are related with the flavor symmetry breaking, the same that is responsible for the stability of DM. We obtain the two textures predicting a vanishing neutrinoless double beta decay at tree level, namely A1 and A2
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