the lepton asymmetry from the decays of per X $^{±}$, highly suppressed by the shined value 〈 χ 〉 . Furthermore, the coupling of χ to ξ and φ will also lead to annihi- lations of N$_{R}$$_{1}$$_{,}$$_{2}$ . Such processes can be suppressed if ξ is much heavier than X $^{±}$, say m$_{ξ}$/M$_{±}$ ∼ 3 − 10. As for the lepton number violating processes mediated by ξ , they will not wash out the produced lepton asymme- try due to the small 〈 χ 〉 . As a result of the symmetry breaking of the global lepton number, there would be a massless Goldstone — majoron [20], which is composed of the imaginary parts of the triplet ξ and the doublet η in our brane, the singlet χ in the bulk and the singlets σ in the distant branes. Because ξ , η and χ with small VEVs only contribute a tiny fraction, this majoron is harmless [21], in particular, it will not significantly affect the annihilation of N$_{R}$$_{1}$$_{,}$$_{2}$ [22]. We now give a numerical estimation. With the input (9), we can obtain with In the weak washout region, i.e. the final baryon asymmetry can be approximately given by [19] by inserting to Eqs. (11), (14), (15) and (23c). We further consider in Eq. (21) and then get We also take Here Γ$_{X}$$_{±}$ is the decay width With the parameter choice (28), (31) and (32), it is easy to derive the CP asymmetry whereas H ( T ) is the Hubble constant and hence the baryon asymmetry The left-handed neutrinos can obtain a Majorana mass matrix with two nonzero eigenvalues from the two right- handed neutrinos N$_{R}$$_{1}$$_{,}$$_{2}$ as a result of inverse [23, 24] seesaw. However, these masses are too tiny to explain the observed neutrino oscillations because of the smallness of the Yukawa couplings y$_{α}$$_{1}$ and y ′ α $_{2}$. Alternatively, our model accommodates the type-II seesaw, with g$_{∗}$ ≃ 106 . 75 being the relativistic degrees of free- dom. We should keep in mind that the right-handed neu- trinos N$_{R}$$_{1}$$_{,}$$_{2}$ , or equivalently the Majorana fermions X ± have Yukawa couplings with the bulk scalar χ . The in- duced annihilations of X ± should go out of equilibrium. This can be achieved if X ± is much lighter than the bulk scalar χ and the triplet scalar ξ . Actually, a fac- tor m$_{χ}$/M$_{±}$ ∼ 3 − 10 is enough for the decoupling of the t-channel processes N c $_{R$_{1}$$_{,}$$_{2}$}$N$_{R}$$_{1}$$_{,}$$_{2}$ → χ $^{∗}$χ which is fast Boltzmann suppressed at temperatures below the mass m$_{χ}$ . In addition, the annihilations of N$_{R}$$_{1}$$_{,}$$_{2}$ to the SM Higgs doublet φ (through the s-channel exchange of χ ) is Here the trilinear coupling µ of the Higgs triplet ξ to the SM Higgs doublet φ is given by the shined value of the bulk field χ , µ = ( κ$_{1}$ + κ$_{2}$ ρ $^{2}$〈 χ 〉 2 m 4 η ) 〈 χ 〉 . (36) L ⊃ − 1 2 f$_{αβ}$ ¯ ψ c $_{L$_{α}$}$iτ$_{2}$ ξψ$_{L}$$_{β}$ − µφ $^{T}$iτ$_{2}$ ξφ + H.c. . (35) H ( T ) = ( π $^{2}$g$_{∗}$ 90 ) 1 2 T 2 M$_{Pl}$ (27) Γ$_{X}$ ± = 1 8 π A$_{X}$ ± M$_{±}$ , (26) n$_{B}$ s = 28 79 n$_{B}$ − n$_{L}$ s = − 28 79 n$_{L}$ s ≃ − 28 79 ε$_{X}$ ± n eq X ± s ∣ T ≃ M$_{±}$ ≃ − 1 O (10) ε$_{X}$$_{±}$ g$_{∗}$ . (25) Γ$_{X}$ ± < H ( T ) ∣ T ≃ M$_{±}$ , (24) x = M 2 $_{+}$− M 2 − M$_{+}$M$_{−}$ . (23c) A$_{X}$$_{−}$ = Σ$_{α}$ | sy$_{α}$$_{1}$ + cy ′ α 2 | 2 , (23b) A$_{X}$ + = Σ$_{α}$ | cy$_{α}$$_{1}$ − sy ′ α 2 | 2 , (23a) ε$_{X}$ ± = Σ$_{α}$ [ Γ( X ± → ψ$_{L}$$_{α}$ + φ $^{∗}$) − Γ( X ± → ψ c L$_{α}$ + φ ) ] Σ$_{α}$ Γ( X ± → ψ$_{L}$$_{α}$ + φ $^{∗}$) + Γ( X ± → ψ c L$_{α}$ + φ ) ≃ sc Σ$_{αβ}$ ( | y$_{α}$$_{1}$ | 2 − | y ′ α $_{2}$| 2 ) 4 πA$_{X}$$_{±}$ × Im ( c $^{2}$y ∗ β $_{1}$y ′ β 2 − s $^{2}$y ′∗ β $_{2}$y$_{β}$$_{1}$ ) x x 2 + 1 64 π 2 A 2 X ∓ (22) M$_{±}$ ≃ 600 GeV and x = O (10 − $^{12}$) (28) M$_{N}$ = 600 GeV and h$_{1}$$_{,}$$_{2}$ ∼ O (10 − $^{3}$) (29) ρ = m$_{η}$ ≲ M$_{∗}$ (30) y ′ α 2 ∼ O (10 − $^{10}$) for y$_{α}$$_{2}$ ∼ O (1) . (31) | y$_{α}$$_{1}$ | = O (10 − $^{7}$) and sin y$_{α}$$_{1}$ | y$_{α}$$_{1}$ | = O (0 . 1) . (32) n$_{B}$ s = O (10 − $^{10}$) . (34) ε$_{±}$ = O (10 − $^{7}$) (33) 3