Plan Z. P. Li, X. C. Lou, Y. N. M. Tung and M. H. Wu, Phys. Rev. D [**43**]{}, (1991) 140. K. Sasaki, N. Sasaki and T. Yanagida, Phys. Lett. B [**494**]{}, 117 (2000). A. D. Linde and D. H. Lyth, Phys. Lett. B [**246**]{}, 353 (1990). K. A. Olive, G. Steigman and T. P. Walker, Phys. Rept.  [**333**]{}, 389 (2000). [^1]: email address: kkohri@eken.phys.nagoya-u.ac.jp [^2]: email address: sakakibara@hiroshima-u.ac.jp [^3]: We have checked the consistency of these results with Ref. [@Sugiyama-etal]. [^4]: Our definition of $Q$ differs from theirs by a factor of $1/\sqrt{2}$. [^5]: We use the notation $B-L$ in place of $L_{3}-L_{4}$, to avoid the confusion with $L_1 - L_2$. [^6]: We have computed a few higher-order corrections for the asymmetry in the $Q$-asymmetry direction. However, because they are not available as a single number, we can not show it here. [^7]: Notice that the difference is of ${\cal O}(\theta^6)$ as compared to the naive estimation in Eq. (\[DeltaN\]). [^8]: This estimation holds as long as $x \gg 1$, which is the case in our analysis. [^9]: We have checked that the mass squared difference and the mixing angle can be determined without loss of precision by only using $\lambda_{3}$ and $\lambda_7$. [^10]: We have checked that the results for $Q$ and $P$ with the potential given by the tree-level approximation is practically the same as that for $\theta_s \simeq 0.1$. [^11]: The mass scale $M_{X}$ is a few times of $10^{10}$ GeV, which is the order of the scale at which the right-handed neutrino is decoupled. [^12]: Since the magnitude of CP-violating parameters for $L$ are fixed to be small from neutrino oscillation data and neutrinoless double beta decay, we ignore them in this subsection. [^13]: In this case, all three light neutrinos have almost degenrate masses, for simplicity, we have ignored the small mass difference among the three light neutrinos. [^14]: We also include the higher order corrections to the neutrino Yukawa coupling matrix given in Eq. (\[NHnu\]). [^15]: Since the CP-violating asymmetry in the direction $N_{2}N_{3}$ is of ${\cal O}(\theta^{6})$, this asymmetry is much smaller than that of $N_{1}N_{3}$.