Distribution of Neutrino Mixing Parameters FromReal and Complex Random Neutrino Mass Matrices

Abstract: The theory of neutrino oscillations is covered. Also, the theory of Dirac, Majorana, and Dirac-Majorana neutrinos is presented. From this theory, and the model presented in [7], a program is constructed which creates a suitable number of neutrino mass matrices M using pseudo-random numbers generated in MATLAB. These matrices are diagonalised, and from the general notion of the Pontecorvo-Maki-Nakagawa-Sakata matrix UPMNS, statistical distributions of six mixing parameters are presented, namely; 12; 13; 23, the CP-violating Dirac phase delta ( ), and two Majorana CP-violating phases alpha one and two ( 1; 2). Furthermore, from the diagonal matrix resulting from the diagonalisation of M, masses mi, of the mass states i; i = 1; 2; 3, are taken. All data is presented in histograms using 90 bins. This numerical approach to determining how the neutrino mixing parameters are distributed will be discussed in section 2.10, and possible conclusions regarding the statistical distributions of the mixing angles 12; 13, and 23, and the masses mi will be presented in chapter 3.