Primordial Lepton Family Asymmtries in Seesaw Model

In leptogenesis scenario, the decays of heavy Majorana neutrinos generate lepton family asymmetries, $Y_e, Y_{\mu}$ and $Y_{\tau}$. They are sensitive to CP violating phases in seesaw models. The time evolution of the lepton family asymmetries are derived by solving Boltzmann equations. By taking a minimal seesaw model, we show how each family asymmetry varies with a CP violating phase. For instance, we find the case that the lepton asymmetry is dominated by $Y_{\mu}$ or $Y_{\tau}$ depending on the choice of the CP violating phase. We also find the case that the signs of lepton family asymmetries $Y_{\mu}$ and $Y_{\tau}$ are opposite each other. Their absolute values can be larger than the total lepton asymmetry and the baryon asymmetry may result from the cancellation of the lepton family asymmetries.