Neutrino Mass Matrix and Hierarchy

• Published in: arXiv.org 2003-02
• Main Authors: Kaus, Peter, Meshkov, Sydney
• Format: Article
• Language: English
• Subjects: Beta decay; Leptons; Mass matrix; Mass ratios; Mathematical models; Neutrinos; Order parameters; Quarks; Supersymmetry
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0211338

We build a model to describe neutrinos based on strict hierarchy, incorporating as much as possible, the latest known data, for \(\Delta_{sol}\) and \(\Delta_{atm}\), and for the mixing angles determined from neutrino oscillation experiments, including that from KamLAND. Since the hierarchy assumption is a statement about mass ratios, it lets us obtain all three neutrino masses. We obtain a mass matrix, \(M_\nu\) and a mixing matrix, \(U\), where both \(M_\nu\) and \(U\) are given in terms of powers of \(\Lambda\), the analog of the Cabibbo angle \(\lambda\) in the Wolfenstein representation, and two parameters, \(\rho\) and \(\kappa\), each of order one. The expansion parameter, \(\Lambda\), is defined by \(\Lambda^2 = m_2/m_3 = \surd (\Delta_{sol}/\Delta_{atm}) \approx\) 0.16, and \(\rho\) expresses our ignorance of the lightest neutrino mass \(m_1, (m_1 = \rho \Lambda^4 m_3\)), while \(\kappa\) scales \(s_{13}\) to the experimental upper limit, \(s_{13} = \kappa \Lambda^2 \approx 0.16 \kappa\). These matrices are similar in structure to those for the quark and lepton families, but with \(\Lambda\) about 1.6 times larger than the \(\lambda\) for the quarks and charged leptons. The upper limit for the effective neutrino mass in double \(\beta\)-decay experiments is \(4 \times 10^{-3} eV\) if \(s_{13} = 0\) and \(6 \times 10^{-3} eV\) if \(s_{13}\) is maximal. The model, which is fairly unique, given the hierarchy assumption and the data, is compared to supersymmetric extension and texture zero models of mass generation.