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Noncommutativity of Lepton Mass Matrices: Flavor Mixing and CP Violation
Author(s) -
Xing Zhizhong
Publication year - 2002
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/1521-3978(200205)50:5/7<569::aid-prop569>3.0.co;2-s
Subject(s) - particle physics , physics , neutrino , lepton , neutrino oscillation , cp violation , mixing (physics) , commutator , pontecorvo–maki–nakagawa–sakata matrix , mass matrix , invariant (physics) , lepton number , sterile neutrino , nuclear physics , mathematical physics , quantum mechanics , lie conformal algebra , lie algebra , electron
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.