Neutrino mass square ratio and neutrinoless double-beta decay in random neutrino mass matrices

We study neutrino mass anarchy in the Dirac neutrino, seesaw, and double-seesaw models. Assuming the anarchy hypothesis, the mass matrices are random and distributed in accordance with the Gaussian measure. We focus on the distributions of the mass square ratio of the light neutrinos and examine which of these models shows a peak in the probability distribution around the experimental value. We show that the peak position depends on the number of random matrix products. We find that the light neutrino mass hierarchy becomes larger as the number of random matrix products is increased and the seesaw model with the random Dirac and Majorana mass matrices is the most likely to realize the current experimental data. We also investigate the distributions of the effective Majorana mass for neutrinoless double-beta decay. We find that the effective Majorana mass is smaller than the experimental upper bound and tends to be smaller as the number of random matrix products increases because the light neutrino masses become more hierarchical. We argue that the tendency for lighter neutrino masses to become more hierarchical as the number of products in the random matrix increases can be understood from the probability distribution of singular values in random matrix theory.