Noncommutativity of Lepton Mass Matrices: Flavor Mixing and CP Violation

  1. Dr. Dietrich Papenfuß2,
  2. Professor Dr. Dieter Lüst3 and
  3. Professor Dr. Wolfgang P. Schleich4
  1. Zhi-Zhong Xing

Published Online: 29 NOV 2007

DOI: 10.1002/9783527610853.ch19

100 Years Werner Heisenberg: Works and Impact

100 Years Werner Heisenberg: Works and Impact

How to Cite

Xing, Z.-Z. (2002) Noncommutativity of Lepton Mass Matrices: Flavor Mixing and CP Violation, in 100 Years Werner Heisenberg: Works and Impact (eds D. Papenfuß, D. Lüst and W. P. Schleich), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527610853.ch19

Editor Information

  1. 2

    Alexander von Humboldt-Stiftung, Bonn, Germany

  2. 3

    Humboldt Universität, Institut für Physik, Germany

  3. 4

    Universität Ulm, Abteilung f. Quantenphysik, Albert-Einstein-Allee 11, 89069 Ulm, Germany

Author Information

  1. Institute of High Energy Physics, P.O. Box 918 (4), Beijing 100039, China

Publication History

  1. Published Online: 29 NOV 2007
  2. Published Print: 27 AUG 2002

ISBN Information

Print ISBN: 9783527403929

Online ISBN: 9783527610853

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Keywords:

  • elementary particles theory;
  • Noncommutativity of Lepton Mass Matrices;
  • flavor mixing;
  • CP violation;
  • four-neutrino mixing scheme;
  • sum rules for the rephasing-invariant measures of leptonic CP violation;
  • T-violating asymmetries;
  • future long-baseline neutrino oscillation experiments

Summary

I follow a lesson learnt from Heisenberg's matrix Quantum Mechanics to study the property of lepton flavor mixing and CP violation. I show that the commutator of lepton mass matrices defined in vacuum keeps invariant under terrestrial matter effects within the four-neutrino mixing scheme. A set of model-independent sum rules for neutrino masses are obtained, and they can be generalized to hold for an arbitrary number of neutrino families. Useful sum rules for the rephasing-invariant measures of leptonic CP violation have also been found. Finally I present a generic formula of T-violating asymmetries applicable to the future long-baseline neutrino oscillation experiments.