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.

19 pages, 7 figures

References in corpus (13)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Observation of electron-antineutrino disappearance at Daya Bay
• Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Neutrino oscillations refitted
• New expectations and uncertainties on neutrinoless double beta decay
• A Bayesian comparison of U(1) lepton flavour models
• Statistical Understanding of Quark and Lepton Masses in Gaussian Landscapes
• Seesaw parametrization for n right-handed neutrinos
• Neutrino Mass Anarchy and the Universe
• Anarchy and Leptogenesis
• Minimally Allowed Neutrinoless Double Beta Decay Rates Within an Anarchical Framework