Perturbative Bottom-up Approach for Neutrino Mass Matrix in Light of Large \theta_{13} and Role of Lightest Neutrino Mass

Abstract

We discuss the role of lightest neutrino mass (m_0) in the neutrino mass matrix, defined in a flavor basis, through a bottom-up approach using the current neutrino oscillation data. We find that if m_0 < 10^{-3} eV, then the deviation \delta M_\nu in the neutrino mass matrix from a tree-level, say tribimaximal neutrino mass matrix, does not depend on m_0. As a result \delta M_\nu's are exactly predicted in terms of the experimentally determined quantities such as solar and atmospheric mass squared differences and the mixing angles. On the other hand for m_0 \gsim 10^{-3} eV, \delta M_\nu strongly depends on m_0 and hence can not be determined within the knowledge of oscillation parameters alone. In this limit, we provide an exponential parameterization for \delta M_\nu for all values of m_0 such that it can factorize the m_0 dependency of \delta M_\nu from rest of the oscillation parameters. This helps us in finding \delta M_\nu as a function of the solar and atmospheric mass squared differences and the mixing angles for all values of m_0. We use this information to build up a model of neutrino masses and mixings in a top-down scenario which can predict large \theta_{13} perturbatively.