Leptogenesis with an almost conserved lepton number

Seesaw models with a slightly broken lepton number symmetry can explain small neutrino masses, and allow for low-scale leptogenesis. We make a thorough analysis of leptogenesis within the simplest model with two right-handed (RH) neutrinos (or with N_3 decoupled). We obtain a semi-analytical formula for the final asymmetry in both supersymmetric and non-supersymmetric cases with a simple dependence on each parameter. The low-energy parameters factorize from the high-energy ones, and the high-energy phase must be non-zero. The role of the PMNS phases is carefully studied. Moreover, we find that the breaking parameter in the Yukawa coupling matrix must be relatively large, \epsilon_h > 10^{-3} for normal and 10^{-2} for inverted hierarchy. Therefore, leptogenesis in our simple model is incompatible with RH neutrino signals at future colliders or sizable lepton-flavor violation. The other breaking parameter, \epsilon_M, which appears in the RH neutrino mass matrix, can be much smaller, and actually needs to be so in order to have low-scale leptogenesis.