For the sake of simplicity, we assume $|a_2|=|b_2|$ and $\Delta = \pi/2$. The CP asymmetry parameter $\epsilon_\mu$ is $$\begin{aligned}
\epsilon_\mu = -\frac{3M_1}{16\pi v^2}\sqrt{\frac{M_1}{M_2}}\frac{|M_{ee}| |a_2|^2}{|M_{ee}|+2 (1+M_1/M_2) |a_2|^2},\end{aligned}$$ and we obtain $$\begin{aligned}
\eta_B=6.1\times 10^{-10},\end{aligned}$$ for $M_1=9.7\times 10^{11}$ GeV, $M_2=100M_1$, $|M_{ee}|=0.069$ eV and $|a_2|=0.063$ eV, which is consistent with the observed value of $\eta_B = (6.02-6.18) \times 10^{-10}$ [@etaB]. More general analysis will be found elsewhere [@New].

\[sec:Appendix\]Useful Constraints
==================================

In this appendix, we describe how to obtain various constraints on $a_{1,+,-}$ and $b_{1,+,-}$ as solutions to the equations, Eqs.(\[Eq:m1=0 for seesaw\])-(\[Eq:13 for NHseesaw\]) for NH and Eqs.(\[Eq:m3=0 for seesaw\])-(\[Eq:13 for IHseesaw\]) for IH. We use constraints on $a_{1,+,-}$ as initial conditions to find our solutions, which can be transformed into other solutions based on those on $b_{1,+,-}$ by the interchange of $a\leftrightarrow b$. The initial setup for $a_{1,+,-}$, where one combination of Dirac neutrino masses to vanish, turns out to be given by $a_1=0$, $a_+=0$, $a_-=0$ or ${{a_ + } + {t_{13}}{a_1}{e^{ - i{\delta _{CP}}}} = 0}$. For NH,

1.  $a_1=0$: From Eq.(\[Eq:m1=0 for seesaw\]), ${a_ - ^2 =  - \left( {{b_ - } - \frac{1}{{{t_{12}}{c_{13}}}}{b_1}} \right){b_ - }}$ is required to have $m_1 = 0$. From Eq.(\[Eq:23 for NHseesaw\]) for $\theta_{23}$ 