Flavor symmetries , leptogenesis and the absolute neutrino mass scale

We study the interplay between flavor symmetries and leptogenesis in the case when the scale of flavor symmetry breaking is higher than the scale at which lepton number is violated. We show that when the heavy Majorana neutrinos belong to an irreducible representation of the flavor group, all the leptogenesis CP asymmetries vanish in the limit of exact symmetry. In the case of reducible representations we identify a general condition that, if satisfied, guarantees the same result. We then focus on the case of a model in which an A4 flavor symmetry yields a drastic reduction in the number of free parameters, implying that at leading order several quantities are only a function of the lightest neutrino mass ml, which in turn is strongly constrained. For normal ordering (NO) we find ml ≃ (0.0044 ÷ 0.0056) eV while for inverted ordering (IO) ml & 0.017 eV. For the 0ν2β decay parameter this yields |mee| ≃ (0.006 ÷ 0.007) eV (NO) and |mee| ∼ 0.017 eV (IO). We show that the leptogenesis CP asymmetries only depend on ml, on a single non-hierarchical Yukawa coupling y, and on two parameters that quantify the flavor symmetry breaking effects, and we argue that the unflavored regime for leptogenesis is strongly preferred in our model, thus realizing a rather predictive scenario. Performing a calculation of the matter-antimatter asymmetry we find that for NO the observed value is easily reproduced for natural values of the symmetry breaking parameters. For IO successful leptogenesis is possible for a limited choice of the parameters implying rather large reheating temperatures Treh & 5× 1013 GeV.