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

TL;DR

This paper demonstrates that a degenerate neutrino mass spectrum can naturally arise in the neutrino mass anarchy framework using Wishart matrices, with implications for neutrinoless double beta decay and CP violation.

Contribution

It introduces a novel realization of degenerate neutrino masses via Wishart matrices within the neutrino mass anarchy hypothesis, analyzing parameter constraints and experimental prospects.

Findings

Degenerate neutrino masses are achievable with Wishart matrices for large N.

Predicted $m_{ee}$ values can be within future experimental reach.

Large N values are compatible with observed neutrino oscillation data.

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.