We propose a new motivation for the stability of dark matter (DM). We suggest that the same nonabelian discrete flavor symmetry which accounts for the observed pattern of neutrino oscillations, spontaneously breaks to a Z2 subgroup which renders DM stable. The simplest scheme leads to a scalar doublet DM potentially detectable in nuclear recoil experiments, inverse neutrino mass hierarchy, hence a neutrinoless double beta decay rate accessible to upcoming searches, while θ13 = 0 gives no CP violation in neutrino oscillations. Introduction The existence of dark matter (DM) plays a central role in the modeling of structure formation and galaxy evolution, affecting also the cosmic microwave background. Despite the strong evidence in favor of DM, its detailed nature remains rather elusive. Viable particle physics candidates for dark matter must be electrically neutral, and provide the correct relic abundance. Therefore they must be stable over cosmological time scales. A simple way to justify the stability of the DM is by assuming some parity symmetry Z 2 , which might arise from the spontaneous breaking of an abelian U(1) gauge symmetry [1-3] 1 , or from a non-abelian discrete symmetry, as might be the case in some string models [4].Non abelian discrete symmetries are motivated by neutrino oscillation data [5,6]. Here we propose that the same symmetry explaining neutrino mixing angles is also responsible for the dark matter stability. In our simplest type-I seesaw [7] realization the flavor symmetry A 4 spontaneously breaks to Z 2 providing a stable DM candidate. We extend the scalar sector of the standard model by adding three Higgs doublets transforming as a triplet of A 4 we show that there is a consistent pattern of vacuum expectation values (vevs) for which only one of the three extra Higgs doublets takes a vev, while the other two give rise to the dark matter candidate. The model accounts for the observed pattern of mixing angles [8] indicated by current neutrino oscillation data, predicting θ 13 = 0 and inverted spectrum of neutrino masses. It will therefore be tested in upcoming double beta and neutrino oscillation searches [9], while the dark matter has potentially detectable rates within reach of nuclear recoil experiments.

The recent results of the Planck experiment put a stringent constraint on the sum of the light neutrino masses, Σ i m i < 0.23 eV (95% CL). On the other hand, two-zero Majorana mass matrix textures predict strong correlations among the atmospheric angle sin 2 θ 23 and Σ. We use the Planck result to show that, for the normal hierarchy case, the texture with vanishing (2, 2) and (3, 3) elements is ruled out at a high confidence level; in addition, we emphasize that a future measurement of the octant of θ 23 (or the 1σ determination of it based on recent fit to neutrino data) will put severe constraint on the possible structure of the Majorana mass matrix. The implication of the above mentioned correlations for neutrinoless double β-decay are also discussed, for both normal and inverted orderings.

In combination with supersymmetry, flavor symmetry may relate quarks with leptons, even in the absence of a grand-unification group. We propose an SU (3) × SU (2) × U (1) model where both supersymmetry and the assumed A4 flavor symmetries are softly broken, reproducing well the observed fermion mass hierarchies and predicting: (i) a relation between down-type quarks and charged lepton masses, and (ii) a correlation between the Cabibbo angle in the quark sector, and the reactor angle θ13 characterizing CP violation in neutrino oscillations.

A class of discrete flavor-symmetry-based models predicts constrained neutrino mass matrix schemes that lead to specific neutrino mass sum-rules (MSR). We show how these theories may constrain the absolute scale of neutrino mass, leading in most of the cases to a lower bound on the neutrinoless double beta decay effective amplitude.Comment: 12 pages, 12 figure