Comparative analysis on the validity of golden ratio, tri-bimaximal, hexagonal and bimaximal neutrino mixing patterns under the radiative corrections

Abstract

We study the comparative analysis on the validity of four popular leptonic mixing patterns viz, golden ratio (GR), tri-bimaximal (TBM), hexagonal mixing (HM) and bimaximal (BM), which are assumed to be defined at high energy scale, M R = 1016 GeV. We perform numerical analysis of low energy neutrino oscillation parameters through the renormalisation group equations (RGEs) in both standard model (SM) and minimal supersymmetric standard model (MSSM) with the inclusion of scale dependent vacuum expectation value (VEV). The sum of three absolute neutrino mass eigenvalues obtained from the latest Planck cosmological data, ∑∣m i ∣ < 0.12 eV, is used as a constraint in the analysis of these four leptonic mixing patterns. We consider both normal hierarchical (NH) model and inverted hierarchical (IH) model in the analysis of these four leptonic mixing patterns, with SUSY breaking scale at m s = 1 TeV and tanβ=67 . Among the four mixing patterns, GR is found to satisfy the latest Planck cosmological data, ∑∣m i ∣ < 0.12 eV. Further analysis on the effect of the variation of SUSY breaking scale 1 TeV ≤ m s ≤ 14 TeV is also studied for GR neutrino mixing pattern in NH.