see in Eq. (22). On the other hand, leptogenesis is associated with both ˜ Y$_{ν}$ itself and the combination of neutrino Dirac Yukawa coupling matrix, H ≡ ˜ Y † ν ˜ Y$_{ν}$ = $_{V}$† $_{R}$Y † $_{ν}$Y$_{ν}$ V$_{R}$ , which is given as where α = e, µ, τ , which implies that both CP phases in M$_{R}$ and Y$_{ν}$ take part in leptogenesis. Due to the Z$_{2}$ symmetry, we can not get the neutrino Dirac masses and therefore the usual seesaw does not operate any more. However, similar to [19] the light neutrino mass matrix can be generated through one-loop diagram showed in Fig. 1 with the quadratic scalar interactions, i.e λ$_{Φ}$$_{η}$ (Φ † η )(Φ † η ). After electroweak symmetry breaking, i.e. 〈 Φ $^{0}$〉 = ( υ, υ, υ ), in a charged lepton mass matrix is diagonal, the flavor neutrino masses can be written as where F ( z$_{i}$ ) = Δ m 2 η 16 π 2 ( z$_{i}$ 1 − z$_{i}$ )[ 1+ z$_{i}$ ln z$_{i}$ 1 − z$_{i}$ ] , Δ m 2 η ≡ | m 2 R − m 2 I | = O ( λ$_{Φ}$$_{η}$ ) υ 2 and z$_{i}$ = M 2 i ¯ m 2 $_{η}$, if m$_{R}$ ( m$_{I}$ ) is the mass of η 0 $_{R}$( η 0 $_{I}$) and m 2 R ( I ) = ¯ m 2 η ± Δ m 2 $_{η}$/ 2 $^{3}$. In our scenario, if we assumed M 2 i ≳ ¯ m 2 $_{η}$, so the lightest Z$_{2}$ -odd neutral particle of η is stable, the above formula Eq. (15) can be ( m$_{ν}$ )$_{αβ}$ = ∑ i ˜ Y$_{ναi}$ ˜ Y$_{νβi}$ M$_{i}$ F ( M 2 i ¯ m 2 η ) , (15) FIG. 1: One-loop generation of light neutrino masses. ν$_{α}$ ν$_{β}$ N$_{i}$ η 0 η 0 Φ 0 Φ 0 III. NEUTRINO MASS MATRIX Im { H$_{ij}$ ( ˜ Y$_{ν}$ $_{)}$∗ $_{αi}$( ˜ Y$_{ν}$ )$_{αj}$ } , with H = g 2 ν    1 + x 2 2 − √$_{2}$$_{xe}$$_{−}$ i ϕ$_{1}$ 2 cos φ − x 2 2 e i ϕ$_{2}$ $^{−}$ϕ$_{1}$ 2 − √$_{2}$$_{xe}$ i ϕ$_{1}$ 2 cos φ 1 + x 2 √$_{2}$$_{xe}$ i ϕ$_{2}$ 2 cos φ − x 2 2 e i ϕ$_{1}$ $^{−}$ϕ$_{2}$ 2 √$_{2}$$_{xe}$$_{−}$ i ϕ$_{2}$ 2 cos φ 1 + x 2 2   $^{.}$ (14) 3 Actually, from potential lagrangian we can fully express the scalar masses m$_{η}$ ± , m$_{R}$, m$_{I}$ and ¯ m$_{η}$ . However, for simplicity, these are expressed in terms of a relevant potential term. 8