Abstract
Using the density matrix equations (DME) for high scale leptogenesis based on the type I seesaw mechanism, in which the CP violation (CPV) is provided by the low-energy Dirac or/and Majorana phases of the neutrino mixing (PMNS) matrix, we investigate the 1-to-2 and the 2-to-3 flavour regime transitions, where the 1, 2 and 3 leptogenesis flavour regimes in the generation of the baryon asymmetry of the Universe ηB are described by the Boltzmann equations. Concentrating on the 1-to-2 flavour transition we determine the general conditions under which ηB goes through zero and changes sign in the transition. Analysing in detail the behaviour of ηB in the transition in the case of two heavy Majorana neutrinos N1,2 with hierarchical masses, M1 ≪ M2, we find, in particular, that i) the Boltzmann equations in many cases fail to describe correctly the generation of ηB in the 1, 2 and 3 flavour regimes, ii) the 2-flavour regime can persist above (below) ∼ 1012 GeV (∼ 109 GeV), iii) the flavour effects in leptogenesis persist beyond the typically considered maximal for these effects leptogenesis scale of 1012 GeV. We further determine the minimal scale M1min at which we can have successful leptogenesis when the CPV is provided only by the Dirac or Majorana phases of the PMNS matrix as well as the ranges of scales and values of the phases for having successful leptogenesis. We show, in particular, that when the CPV is due to the Dirac phase δ, there is a direct relation between the sign of sin δ and the sign of ηB in the regions of viable leptogenesis in the case of normal hierarchical light neutrino mass spectrum; for the inverted hierarchical spectrum the same result holds for M1 ≲ 1013 GeV. The considered different scenarios of leptogenesis are testable and falsifiable in low-energy neutrino experiments.
Involution symmetries and the PMNS matrix
