Deviations from Tribimaximal and Golden Ratio mixings under radiative corrections of neutrino masses and mixings

Abstract: The impact of renormalization group equations(RGEs) on neutrino masses and mixings at high energy scales in Minimal Supersymmetric Standard Model(MSSM) is studied using two different mixing patterns such as Tri-Bimaximal(TBM) mixing and Golden Ratio(GR) mixing in consistent with cosmological bound of the sum of three neutrino masses, $\sum {i}|m{i}|$. Magnifications of neutrino masses and mixing angles at low energy scale, are obtained by giving proper input masses, and mixing angles from TBM mixing matrix and GR mixing matrix at high energy scales. High energy scales, $M_{R}$ such as $10^{13}$GeV,$10^{14}$GeV,$10^{15}$GeV are employed in the analysis. The large solar($\theta_{12}$) and atmospheric($\theta_{23}$) neutrino mixing angles with zero reactor angle ($\theta_{13}$) from both TBM mixing matrix and GR mixing matrix at high scale, can magnify the reactor angle($\theta_{13}$) at low energy scale in 3$\sigma$ confidence level. Both cases of normal hierarchy(NH) and inverted hierarchy(IH) are addressed here. In normal hierarchical case, it is found that $\theta_{23}\simeq51.1^{\circ}$ and that in inverted hierarchical case is $\theta_{23}\simeq39.1^{\circ}$ in both mixing patterns. Possibility of $\theta_{23}>45^{\circ}$ or $\theta_{23}<45^{\circ}$ is observed at low scale. The analysis shows the validity of the two mixing patterns at high energy scale.