Neutrino masses and mixing from hierarchy and symmetry

We construct a model that allows us to determine the three neutrino masses and the mass matrix directly from the experimental mass squared differences delta atm and delta sol, using the assumptions of rational hierarchy (m1/m2 = m2/m3) and of S3-S2 symmetry for the mixing matrix. We find that both t...

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Bibliographic Details
Published in:arXiv.org 2004-10
Main Authors: Kaus, Peter, Meshkov, Sydney
Format: Article
Language:English
Subjects:
Clebsch-Gordan coefficients
Mass matrix
Mass ratios
Mathematical models
Matrix methods
Neutrinos
Parameters
Symmetry
Online Access:Get full text
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Summary:We construct a model that allows us to determine the three neutrino masses and the mass matrix directly from the experimental mass squared differences delta atm and delta sol, using the assumptions of rational hierarchy (m1/m2 = m2/m3) and of S3-S2 symmetry for the mixing matrix. We find that both the mass ratios and mixing angles are dominated by the same parameter. For the mixing angles, this parameter=sq rt (1/6)=0.41, is a Clebsch-Gordan coefficient. For the masses, the mass ratios depend on the experimental mass squared differences and with most recent data, remarkably, we obtain sq rt (m1/m2)=sq rt (m2/m3)=0.41. This possibly coincidental equality gives a simple mass matrix. We obtain the masses m1,m2 and m3. We also obtain the mass matrix M and evaluate its elements numerically for the presently 'best fit' solution.
ISSN:2331-8422
DOI:10.48550/arxiv.0410024