Simple A4 models for dark matter stability with texture zeros

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