Cosmological family asymmetry andCPviolation

Abstract

We discuss how the cosmological baryon asymmetry can be achieved by the lepton family asymmetries of heavy Majorana neutrino decays and how the lepton family asymmetries are related to $CP$ violation in neutrino oscillation, in the minimal seesaw model with two heavy Majorana neutrinos. We derive the most general formula for $CP$ violation in neutrino oscillation in terms of the heavy Majorana masses and Yukawa mass term. It is shown that the formula is very useful to classify several models in which $e$, $\ensuremath{\mu}$, and $\ensuremath{\tau}$ leptogenesis can be separately realized and to see how they are connected with low energy $CP$ violation. To make the models predictive, we take texture with two zeros in the Dirac matrix. In particular, we find some interesting cases in which $CP$ violation in neutrino oscillation can happen while lepton family asymmetries do not exist at all. On the contrary, we can find $e$-, $\ensuremath{\mu}$-, and $\ensuremath{\tau}$-leptogenesis scenarios in which the cosmological $CP$ violation and low energy $CP$ violation measurable via neutrino oscillations are very closely related to each other. By determining the allowed ranges of the parameters in the models, we predict the sizes of $CP$ violation in neutrino oscillation and $|{V}_{e3}^{\mathrm{MNS}}|$. Finally, the leptonic unitarity triangles are reconstructed.