M ( a, 1 , b ) = ( M$_{1}$, M$_{2}$, M$_{3}$ ) respectively. Note that the overall scale of neutrino masses is determined by g 2 $^{$_{ν}$m}$− as will be shown in Eq. (32), while the magnitudes of function f ( α M ¯ $_{m$_{η}$}$) does not change a lot within the parameter region as we showed in Fig. 2. The neutrino spectrums are related to the ratio M ¯ m$_{η}$ and the value of α , and α = 1 corresponds to the mass of the second generation of light neutrinos m$_{2}$ . The locations of m$_{1}$ and m$_{3}$ are determined by the values of α ′ s (or a, b ) which are defined in Eq. (9), and the constraints come from the solar and atmospheric mass-squared differences. They are given by in which, from the neutrino oscillation experiments we know that Δ m 2 21 is positive and dictates ω$_{2}$ > ω$_{1}$/a with the second term being sufficiently small x in Eq. (29). As will be shown later, in order for a leptogenesis to be successfully implemented at or around TeV scale in our scenario, we consider the case M 2 lightest ≃ ¯ m 2 η where the M$_{lightest}$ is the lightest of the heavy Majorana neutrino. Depending on the hierarchy of the heavy Majorana neutrino masses M$_{1}$ , M$_{2}$ and M$_{3}$ , the relative size of the parameter κ consistent with the possible mass ordering of light neutrinos and hierarchy of Δ m 2 32 and Δ m 2 21 can be classified as follows: 12 Δ m 2 21 ≡ m 2 − m 2 1 ≃ m 2 0 { ω 2 − ω 2 1 a 2 + x 2 ( ω$_{2}$ + ω$_{1}$ a ) $^{2}$cos φ } , (29) Δ m 2 32 ≡ m 2 3 − m 2 ≃ m 2 0 { ω 2 3 b 2 − ω 2 − x 4 ( ω$_{2}$ + ω$_{1}$ a ) $^{2}$cos φ } , (30) FIG. 2: Neutrino mass ordering in different values of M ¯ m$_{η}$ = 1 . 001 , 1 . 25 , 1 . 6 , 100, which correspond to Case-II , Case-III,V , Case-IV , Case-I , respectively. m$_{2}$ m$_{2}$ m$_{2}$ m$_{2}$ Case-IV Case-II Case-III,V Normal hierarchy (Case-I) Quasi-degenerate 0 1 2 3 4 5 Α 0.002 0.004 0.006 0.008 0.010 f $_{Α}$M m$_{Η}$