LMA MSW Solution from the Inverted Hierarchical Model of Neutrinos

Abstract

We examine whether the inverted hierarchical model of neutrinos is compatible with the explanation of the large mixing angles (LMA)MSW solution of the solar neutrino problem. The left-handed Majorana neutrino mass matrix for the inverted hierarchical model, is generated through the seesaw mechanism using the diagonal form of the Dirac neutrino mass matrix and the non-diagonal texture of the right-handed Majorana mass matrix. In a model independent way, we construct a specific form of the charged lepton mass matrix having a special structure in 1-2 block, which contribution to the leptonic mixing (MNS) matrix leads to the predictions $\sin^{2}2\theta_{12}=0.8517$, $\sin^{2}2\theta_{23}=0.9494$, and $|V_{e3}|=0.159$ at the unification scale. These predictions are found to be consistent with the LMA MSW solution of the solar neutrino problem. The inverted hierarchical model is also found to be stable against the quantum radiative corrections in the MSSM. A numerical analysis of the renormalisation group equations (RGEs) in the MSSM shows a mild decrease of the mixing angles with the decrease of energy scale and the corresponding values of the neutrino mixings at the top-quark mass scale are found as $\sin^{2}2\theta_{12}=0.8472$, $\sin^{2}2\theta_{23}=0.9399$, $|V_{e3}|=0.1509$ respectively.