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lepton flavor α (= e, µ, τ ), by [20, 21] 

<img src='content_image/333474.jpg'>

where the function g ( x ) is given by 

<img src='content_image/333473.jpg'>

Here i denotes a generation index and Γ( N$_{i}$ → · · · ) is the decay width of the i th-generation right-handed neutrino. Note that in our scenario the CP asymmetry is generated by ex- plicitly breaking the tri-bimaximal as in Eq. (8) when x is different from zero. Below temperature T ∼ M$_{i}$ ≲ 10 5 GeV, it is known that electron, muon and tau charged lepton Yukawa interactions are much faster than the Hubble expansion parameter rendering the e , µ and τ Yukawa couplings in equilibrium. Then, the processes which wash out lepton num- ber are flavor dependent and thus the lepton asymmetries for each flavor should be treated separately with different wash-out factors. Once the initial values of ε α i are fixed, the final result of η$_{B}$ or Y$_{B}$ can be obtained by solving a set of flavor-dependent Boltzmann equations including the decay, inverse decay, and scattering processes as well as the nonperturbative sphaleron interaction. 

In order to estimate the wash-out effects, we introduce the parameters K α i which are the wash-out factors due to the inverse decay of the Majorana neutrino N$_{i}$ into the lepton flavor α (= e, µ, τ ) [24]. The explicit form of K α i is given by 

<img src='content_image/333472.jpg'>

