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 based on the A_4 flavor symmetry, showing that for normal hierarchy the lightest neutrino mass has to lie within the narrow range m_l \simeq (0.0044 - 0.0056) eV, while for inverted hierarchy m_l \gtrsim 0.017 eV. After showing that the CP asymmetries depend just on one independent phase, we perform a calculation of the matter-antimatter asymmetry within leptogenesis. Since the spectrum of right-handed neutrino masses is above 10^12 GeV, light flavor effects can be neglected but heavy flavor effects must be taken into account. We write the general set of Boltzmann equations, showing that in the case of A_4 the dynamics of the three heavy flavors approximately decouple. Despite of the tight restrictions on the involved parameters, it is intriguing that the observed matter-anti matter asymmetry is naturally reproduced for normal hierarchical neutrino masses. On the other hand, in the case of inverted ordering, successful A_4-leptogenesis is possible for a limited choice of the parameters implying quite large reheating temperatures T_reh\gtrsim 5*10^13 GeV.