Degenerate spectrum in the neutrino mass anarchy with Wishart matrices and implications for $0\nu \beta \beta$ and ${\delta }_{\mathrm{CP}}$

Abstract

We show that a degenerate neutrino mass spectrum can be realized in the neutrino mass anarchy hypothesis, if the neutrino Yukawa and right-handed neutrino mass matrices are given by the Wishart matrix, i.e. products of $N\times 3$ rectangular random matrices, whose eigenvalue distribution tends to degenerate for large $N$. The mixing angle and CP phase distributions are determined by either the Haar measure of U(3) or that of SO(3). We study how large $N$ is allowed to be without tension with the observed neutrino mass squared differences, and find that the predicted value of $m_{ee}$ can be within the reach of future $0\nu \beta \beta$ experiments especially for $N$ on the high side of the allowed range.

Comments: 19 pages, 7 figures