Electroweak naturalness in the three-flavor type I seesaw model and implications for leptogenesis

In the type I seesaw model, the naturalness requirement that corrections to the electroweak μ parameter not exceed 1 TeV results in a rough bound on the lightest right-handed neutrino mass, M_N₁3×10⁷ GeV. In this paper we derive generic bounds applicable in any three-flavor type I seesaw model. We find M_N₁4×10⁷ GeV and M_N₂7×10⁷ GeV. In the limit of one massless neutrino, there is no naturalness bound on M_N₃ in the Poincar\'e protected decoupling limit. Our results confirm that no type I seesaw model can explain the observed neutrino masses and baryogenesis via hierarchical (N₁-, N₂-, or N₃-dominated) thermal leptogenesis while remaining completely natural.