effect on $\epsilon_i$ in the expanding universe is controlled by $$\begin{aligned}
    \eta(x) = \left( \frac{8.25\times 10^{-3} {\rm eV}}{x} + \left( \frac{x}{2\times 10^{-4} {\rm eV}} \right)^{1.16} \right)^{-1},\end{aligned}$$ and $g_\ast$ denotes the effective number of relativistic degree of freedom. We take $g_\ast = 106.75$.

-   The baryon-photon ratio $\eta_B$ is estimated to be $\eta_B=7.04Y_B$.

Next, we estimate the baryon-photon ratio by assuming the maximal CP violation and the maximal atmospheric neutrino mixing in the neutrino sector: e.g., $a_1={\rm real}$, $b_1={\rm real}$, $a_3=-\sigma a_2^\ast$ and $b_3=-\sigma b_2^\ast$. In this case, there are only two independent phases ${\rm arg}(a_2)$ and ${\rm arg}(b_2)$. The CP asymmetry parameter $\epsilon_i$ are obtained as $$\begin{aligned}
\epsilon_e &=& 0,  \nonumber \\
\epsilon_\mu &=&  -\frac{3M_1}{16\pi v^2}\frac{(|a_1||b_1| + 2{\rm Re}[a_2^\ast b_2] ){\rm Im}[a_2^\ast b_2]}{|a_1|^2+2 \vert a_2 \vert^2} \nonumber \\
&=&  -\frac{3M_1}{16\pi v^2}\frac{(|a_1||b_1| + 2|a_2||b_2|\cos\Delta)|a_2||b_2|\sin\Delta}{|a_1|^2+2 |a_2|^2}, \nonumber \\
\epsilon_\tau &=& -\epsilon_\mu,
\label{Eq:epsilon_maxCP_maxAtm}\end{aligned}$$ where $$\Delta = {\rm arg}(b_2)-{\rm arg}(a_2). 
\label{Eq:Delta}$$ From Eq.(\[Eq:epsilon\_maxCP\_maxAtm\]), as we expected, the phase difference $\Delta$ has crucial role in the baryon asymmetry generation in the universe and $\Delta \neq n\pi$ $(n=0, \pm 1, \pm 2 \cdots)$ is required for nonvanishing baryon-photon ratio.

To confirm results of our discussions more concretely, we estimate the CP asymmetry parameters shown in Eq.(\[Eq:epsilon\_maxCP\_maxAtm\]) 