See-saw geometry and leptogenesis

Abstract

The representation of the see-saw 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 ) ≳ 10 11 ( 10 10 ) GeV . The window 10 9 GeV ≲ M 1 , T reh ≲ 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.