Neutrino Mass Matrices with Two Texture Zeros

Abstract

Neutrinos are elementary particles that often travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect. Neutrinos are created as a result of certain types of radioactive decay (beta decay) or nuclear reactions such as those that take place in the Sun, in nuclear reactors, or when cosmic rays hit atoms. Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo in which a neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates. Neutrino oscillation is of theoretical and experimental interest since observation of the phenomenon implies that the neutrino has a non-zero mass. Solar neutrino, atmospheric neutrino, reactor neutrino experiments confirm the phenomenon of oscillations and the existence of neutrino mass. The present experimental data is already sufficient to constraint or test theoretical models of neutrino mass matrix. For example, the present data does not support any neutrino mass matrix with three or more texture zeros. Further, there can be only 15 independent neutrino mass matrices with two texture zeros (6C2 = 15) and only 7 out of the 15 are compatible with the oscillation data. The physically allowed 7 mass matrices can be further divided into three classes: (A) Hierarchical Solutions : |m1| < |m2| ≪ |m3|. The mass matrices are A1 and A2. (B) Degenerate Solutions : The mass matrices B1, B2, B3 and B4 show degeneracy i.e. masses are are approximately equal and they do not support the bimaximal case. 56 (C) Inverted Hierarchy : The mass matrix C has the inverted hierarchy of neutrino masses. In chapter 2, it was shown that predictions of neutrino mass matrices within a class are experimentally indistinguishable. For example the mass matrices A1 and A2 will have identical predictions. Similarly, the mass matrices of type B1 B2, B3 and B4 are same physically. This leads to a degeneracy in the neutrino mass matrices with two texture zeros. Later, we find in Chapter 3 that the predictions are same within a class only for the measured neutrino parameters. As we will have measurements of presently unknown neutrino parameters in the future experiments, we will be able to lift the degeneracy which is present in the neutrino mass matrices with two texture zeros.