Perturbative bottom-up approach for neutrino mass matrix in light of large θ13 and role of lightest neutrino mass

Abstract

We discuss the role of lightest neutrino mass (m0) 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 m0 < 10-3 eV , then the deviation δMν in the neutrino mass matrix from a tree-level, say tribimaximal neutrino mass matrix, does not depend on m0. As a result δMν'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 m0 ≳10-3 eV , δMν strongly depends on m0 and hence cannot be determined within the knowledge of oscillation parameters alone. In this limit, we provide an exponential parametrization for δMν for all values of m0 such that it can factorize the m0 dependency of δMν from rest of the oscillation parameters. This helps us in finding δMν as a function of the solar and atmospheric mass squared differences and the mixing angles for all values of m0. We use this information to build up a model of neutrino masses and mixings in a top-down scenario which can predict large θ13 perturbatively.