R ≈ b $^{2}$(4 ω 2 − ω 2 $_{1}$) , (31) 13 Note here that in our scenario the inverted hierarchical light neutrino mass spectrum is not allowed because the condition Δ m 2 21 > 0 is not satisfied due to the mass ordering of heavy Majorana neutrinos Eq. (9) corresponding to light neutrino mass ordering. In the expressions of Eqs. (24-30), the values of parameters κ (or a, b ), x, φ can be determined from the analysis described in above, whereas g$_{ν}$ is arbitrary. However, since m$_{0}$ = Δ m 2 $_{η}$g 2 $_{ν}$/ 16 π $^{2}$M as defined in Eq. (19), the value of g$_{ν}$ depends on the magnitude of $^{m}$− in the case that m$_{0}$ • Case-I M$_{1}$$_{,}$$_{2}$ ≫ M$_{3}$ ( a > 1 ≫ b with ξ = 0): this case corresponds to the normal hierarchical mass spectrum with b → 0 i.e. κ ≃ 1. Using ω$_{1}$ ≃ 2 ln 2 b − 1, ω$_{2}$ ≃ − 2 ln b − 1 and ω$_{3}$ ≃ 1 $_{2}$, the ratio of the mass squared differences defined by R ≡ Δ m 2 21 | Δ m 2 32 | which is around R ≃ 3 × 10 − 2 for the best-fit values of the solar and atmospheric mass squared differences, which is given by • Case-II M$_{1}$ > M$_{3}$ > M$_{2}$ ( a > b > 1 with ξ = 0): this corresponds to ω 3 b > ω$_{2}$ ≳ ω 1 a , the solution exists for ω 1 a going to ω$_{2}$ ≃ 1 2 giving a ≃ 4 . 7 and b ≃ 2 . 7 with κ ≃ 3 . 7 in numerical calculations, and gives a degenerate normal ordering of light neutrinos. • Case-III M$_{3}$ > M$_{2}$ > M$_{1}$ ( b > 1 ≳ a with ξ = π ): this corresponds to a degenerate inverted ordering of light neutrinos giving a ≃ 1 , b ≃ 3 with κ ≃ 2 in numerical calculations. • Case-IV M$_{1}$ > M$_{2}$ > M$_{3}$ ( a > 1 > b with ξ = 0): this case gives a ≃ 1 . 4 and b ≈ 0 . 6 with κ ≃ 0 . 4 in numerical calculations, which corresponds to ω$_{2}$ ≳ ω 1 a ≳ ω 3 b indicating a degenerate inverted ordering of light neutrinos. • Case-V M$_{1}$ > M$_{2}$ ≳ M$_{3}$ ( a > 1 ≳ b with ξ = 0): this case gives a ≃ 2 . 8 , b ≃ 0 . 8 with κ ≃ 1 . 8 in numerical calculations, which corresponds to ω$_{2}$ ≳ ω 1 a ≳ ω 3 b indicating a degenerate inverted ordering of light neutrinos. where the equality roughly can be given under 1 ≫ x, b . Note here that using the best-fit value of R ( ≃ 3 × 10 − $^{2}$) and Eq. (31) one can roughly determine the size of the parameter b , i.e b ≃ 0 . 01.