content_image/405003.jpg content_image/405002.jpg content_image/405001.jpg content_image/405000.jpg content_image/404999.jpg content_image/404998.jpg content_image/404997.jpg content_image/404996.jpg content_image/405008.jpg content_image/404995.jpg content_image/405004.jpg content_image/405005.jpg content_image/405006.jpg content_image/405007.jpg content_image/405010.jpg content_image/405009.jpg content_image/404994.jpg
the lepton asymmetry from the decays of per X $^{±}$, 

<img src='content_image/405003.jpg'>

with 

In the weak washout region, i.e. 

the final baryon asymmetry can be approximately given by [19] 

Here Γ$_{X}$$_{±}$ is the decay width 

whereas H ( T ) is the Hubble constant 

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 

<img src='content_image/405002.jpg'>

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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 

by inserting 

to Eqs. (11), (14), (15) and (23c). We further consider 

in Eq. (21) and then get 

We also take 

<img src='content_image/405008.jpg'>

With the parameter choice (28), (31) and (32), it is easy to derive the CP asymmetry 

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, 

<img src='content_image/404995.jpg'>

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 , 

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