Implication of cosmological upper bound on the validity of golden ratio neutrino mixings under radiative corrections

Abstract

We study the implication of the most recent cosmological upper bound on the sum of three neutrino masses, on the validity of the golden ratio (GR) neutrino mixings defined at high energy seesaw scale, considering the possibility for generating low energy values of neutrino oscillation parameters through radiative corrections in the minimal supersymmetric standard model (MSSM). The present study is consistent with the most stringent and latest Planck data on cosmological upper bound, $\sum |m_{i}| < 0.12$ eV. For the radiative generation of sin$\theta_{13}$ from an exact form of golden ratio (GR) neutrino mixing matrix defined at high seesaw energy scale, we take opposite CP parity mass eigenvalues ($m_{1},-m_{2},m_{3}$) with a non-zero real value of $m_{3}$, and a larger value of $\tan\beta > 60$ in order to include large effects of radiative corrections in the calculation. The present analysis including the CP violating Dirac phase and SUSY threshold corrections, shows the validity of golden ratio neutrino mixings defined at high seesaw energy scale in the normal hierarchical (NH) model. The numerical analysis with the variations of four parameters viz. $M_{R}$, $m_{s}$, $\tan\beta$ and $\bar{\eta_{b}}$, shows that the best result for the validity is obtained at $M_{R}=10^{15}$ GeV, $m_{s}=1$ TeV, $\tan\beta=68$ and $\bar{\eta_{b}}=0.01$. However, the analysis based on inverted hierarchical (IH) model does not conform with this latest Planck data on cosmological bound but it still conforms with earlier Planck cosmological upper bound $\sum |m_{i}|< 0.23$ eV, thus indicating possible preference of NH over IH models.