Existence of Neutrino Mass : A New Mathematical Formulation

Abstract

It is assumed that there exists a transformation law, even in the standard model framework, that transforms mass eigen states of neutrino to the flavour eigen states. The transformation matrix from mass eigen states to flavor states is assumed to be singular and therefore becomes unable to generate any mass of the neutrino. It is considered that a small deviation from that singular matrix leads to unitary PMNS matrix, which is able to diagonalize the mass matrix. A formulation is done to indicate the possible spontaneous symmetry breaking which can generate physical neutrino mass in eV scale. A mapping between symmetry transformations and a set of real numbers (0,k) is defined on the backdrop of the neutrino mass generation.