Perturbed invariant under a cyclic permutation with trace of neutrino mass matrix remain constant

We construct a neutrino mass matrix $M_ν$ via a seesaw mechanism whith perturbed invariant under a cyclic permutation by introducing one parameter $δ$ into the diagonal elements of $M_ν$ with assumption that trace of the perturbed $M_ν$ is equal to trace of the unperturbed $M_ν$. We found that the perturbed neutrino mass matrices $M_ν$ can predicts the mass-squared difference $Δm_{ij}^{2}\neq 0$ with the possible hierarchy of neutrino mass is normal or inverted hierarchy. By using the advantages of the mass-squared differences and mixing parameters data from neutrino oscillaton experiments, we obtained neutrino masses in inverted hierarchy with masses: $|m_{1}|=0.101023$ eV, $|m_{2}|=0.101428$ eV, and $|m_{3}|=0.084413$ eV.

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