associated with N$_{2}$ and the lepton flavors α = e, µ, τ are given as in which ε µ 2 + ε τ 2 = − ε e 2 is satisfied due to Im[ H$_{2}$$_{j}$ ] = 0 for ϕ$_{1}$$_{,}$$_{2}$ = 0. From Eq. (50) we see that all K -factors are almost equal, so this case can be classified as K α 2 ≥ 1 and K α 2 < 1. In strong wash-out regime K α 2 ≥ 1 ( α = e, µ, τ ), given the initial thermal abundance of N$_{2}$ and the condition for K α $_{2}$, the resulting baryon-to-photon ratio η$_{B}$ approximately given as where x sin φ is from the common factor in K µ,τ 2 . In weak wash-out regime K α 2 < 1 ( α = e, µ, τ ), the resulting baryon-to-photon ratio η$_{B}$ can be simply given as where x sin φ comes from the common factor in K µ,τ 2 , K µ 2 ≃ K τ 2 and K$_{2}$ = K e 2 + K µ 2 + K τ $_{2}$. If we take, for example, δ$_{N}$$_{3}$$_{η}$ = 1 . 5 × 10 − $^{6}$, the magnitude of washout factors are given as and Eq. (52) can be simplified as where g$_{ν}$ ≃ 0 . 4 , b ≃ 2 . 7 and ( K µ $_{2}$) − 1 . 16 ≃ 0 . 2. Fig. 10 shows the behavior of η$_{B}$ as functions of φ and x , representing only in the limit of φ = 3 π/ 2 the value of x can become order of O (0 . 1). However, Fig. (10) shows that η$_{B}$ is not enough for BAU to be satisfied. 24 K e 2 ≃ g 2 $^{$_{ν}$m}$∗ 3 M (1 + 2 x cos φ ) δ 2 N 2 η , K µ 2 ≃ g 2 $^{$_{ν}$m}$∗ 3 M (1 − x cos φ − $_{x}$√$_{3 sin}$$_{φ}$$_{)}$$_{δ}$ 2 N 2 η , K τ 2 ≃ g 2 $^{$_{ν}$m}$∗ 3 M (1 − x cos φ + $_{x}$√$_{3 sin}$$_{φ}$$_{)}$$_{δ}$ 2 N 2 η , (50) where the common factor g 2 $_{ν}$m ∗ M ≃ 8 π $^{$^{2}$m}$∗ m$_{0}$/ ( ¯ m$_{η}$$^{m}$− ), all K -factors are evaluated at tempera- ture T = M$_{2}$ , and M$_{2}$ is the lightest of the heavy Majorana neutrinos. And the corresponding CP asymmetries ε α 2 are approximately given, for x ≪ 1, by ε e 2 = ( b − a ) x $^{2}$g2 ν 32 abπ sin 2 φ , ε µ 2 ≃ xg 2 ν 32 abπ {− 2 $_{a}$√$_{3 +}$ x ( a − b $_{)(}$√$_{3 cos}$$_{φ}$$_{+ sin}$$_{φ}$$_{)}$ } cos φ , ε τ 2 ≃ xg 2 ν 32 abπ { 2 $_{a}$√$_{3}$ − x ( a − b $_{)(}$√$_{3 cos}$$_{φ}$ − sin φ ) } cos φ , (51) η$_{B}$ ≃ $_{10}$− $^{2}$( ε τ 2 − ε µ $_{2}$) x sin φ ( K µ $_{2}$) 1 . 16 , (52) η$_{B}$ ≃ − 3 . 2 × $_{10}$− $^{3}$( ε τ 2 − ε µ $_{2}$) K$_{2}$K µ $_{2}$x sin φ , (53) K e 3 = 3 − 3 . 7 , K µ 3 = 3 − 4 . 9 , K τ 3 = 2 . 2 − 3 . 7 . (54) η$_{B}$ ≃ 4 × $_{10}$− $^{6}$x$^{2}$sin 2 φ , (55)