Seesaw geometry and leptogenesis
  The representation of the seesaw orthogonal matrix in the complex plane establishes a graphical correspondence between neutrino mass models and geometrical configurations, particularly useful to study relevant aspects of leptogenesis. We first derive the CP asymmetry bound for hierarchical heavy neutrinos and then an expression for the effective leptogenesis phase, determining the conditions for maximal phase and placing a lower bound on the phase suppression for generic models. Reconsidering the lower bounds on the lightest right-handed (RH) neutrino mass M_1 and on the reheating temperature T_reh, we find that models where one of the two heavier neutrino masses is dominated by the lightest right-handed (RH) neutrinos, typically arising from connections with quark masses, undergo both phase suppression and strong wash-out such that M_1 (T_reh)\gtrsim 10^{11} (10^{10}) GeV. The window 10^9 GeV \lesssim M_1,T_reh \lesssim 10^{10}GeV is accessible only for a class of models where m_1 is dominated by the lightest RH neutrino, with no straightforward connections with quark masses. Within this class we describe a new scenario of thermal leptogenesis where the baryon asymmetry of the Universe is generated by the decays of the second lightest RH neutrino, such that the lower bound on M_1 disappears and is replaced by a lower bound on M_2. Interestingly, the final asymmetry is independent on the initial conditions. We also discuss the validity of the approximation of hierarchical heavy neutrinos in a simple analytical way. 
Pasquale Di Bari