Tri-Resonant Leptogenesis in a Seesaw Extension of the Standard Model

We study a class of leptogenesis models where the light neutrinos acquire their observed small masses by a symmetry-motivated construction. This class of models may naturally include three nearly degenerate heavy Majorana neutrinos that can strongly mix with one another and have mass differences comparable to their decay widths. We find that such a tri-resonant heavy neutrino system can lead to leptonic CP asymmetries which are further enhanced than those obtained in the usual bi-resonant approximation. Moreover, we solve the Boltzmann equations by paying special attention to the temperature dependence of the relativistic degrees of freedom of the plasma. The latter results in significant corrections to the evolution equations for the heavy neutrinos and the lepton asymmetry that have been previously ignored in the literature. We show the importance of these corrections to accurately describe the dynamical evolution of the baryon-to-photon ratio $\eta_B$ for heavy neutrino masses at and below $100$ GeV, and demonstrate that successful leptogenesis at lower masses can be significantly affected by the variation of the relativistic dofs. The parameter space for the leptogenesis model is discussed, and it could be probed in future experimental facilities searching for charged lepton flavour violation and heavy neutrinos in future $Z$-boson factories.