Covariant extremisation of flavour-symmetric Jarlskog invariants and the neutrino mixing matrix

We examine the possibility that the form of the lepton mixing matrix can be determined by extremising the Jarlskog flavour invariants associated, e.g. with the commutator (C) of the lepton mass matrices. Introducing a strictly covariant approach, keeping masses fixed and extremising the determinant...

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Bibliographic Details
Published inPhysics letters. B Vol. 628; no. 1-2; pp. 93 - 105
Main Authors Harrison, P.F., Scott, W.G.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 03.11.2005
Elsevier Science
Subjects
Exact sciences and technology
Nuclear physics
Physics
The physics of elementary particles and fields
P invariance
Invariant
Mixing
Leptons
Elementary particle mass
Mathematical commutator
Covariant theory
Flavor
Lepton mass
C invariance
Linear combination
Neutrinos
Determinants
CP invariance
Mass matrix
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Summary:We examine the possibility that the form of the lepton mixing matrix can be determined by extremising the Jarlskog flavour invariants associated, e.g. with the commutator (C) of the lepton mass matrices. Introducing a strictly covariant approach, keeping masses fixed and extremising the determinant (Tr C3/3) leads to maximal CP violation, while extremising the sum of the 2×2 principal minors (−TrC2/2), leads to a non-trivial mixing with zero CP violation. Extremising, by way of example, a general linear combination of two CP-symmetric invariants together, we show that our procedures can lead to acceptable mixings and to non-trivial predictions, e.g., |Ue3|≃2/3Δm122/Δm232(1−mμ/mτ)2≃0.07.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2005.09.009