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Informationally Complete Characters for Quark and Lepton Mixings

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Institut FEMTO-ST CNRS UMR 6174, Université de Bourgogne/Franche-Comté, 15 B Avenue des Montboucons, F-25044 Besançon, France
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Quantum Gravity Research, Los Angeles, CA 90290, USA
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Author to whom correspondence should be addressed.
Symmetry 2020, 12(6), 1000; https://doi.org/10.3390/sym12061000
Received: 13 May 2020 / Revised: 5 June 2020 / Accepted: 9 June 2020 / Published: 11 June 2020
(This article belongs to the Special Issue Flavour Problem and Family Symmetry Beyond the Standard Model)
A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters κ of a finite group G. Here, we introduce a d-dimensional Hilbert space with d = c c ( G ) , the number of conjugacy classes of G. Groups under consideration should follow two rules, (a) the character table contains both two- and three-dimensional representations with at least one of them faithful and (b) there are minimal informationally complete measurements under the action of a d-dimensional Pauli group over the characters of these representations. Groups with small d that satisfy these rules coincide in a large part with viable ones derived so far for reproducing simultaneously the CKM (quark) and PNMS (lepton) mixing matrices. View Full-Text
Keywords: informationally complete characters; quark and lepton mixings; CP violation; Pauli groups informationally complete characters; quark and lepton mixings; CP violation; Pauli groups
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Planat, M.; Aschheim, R.; Amaral, M.M.; Irwin, K. Informationally Complete Characters for Quark and Lepton Mixings. Symmetry 2020, 12, 1000.

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