Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2005-07-31
Phys.Lett. B628 (2005) 93
Physics
High Energy Physics
High Energy Physics - Phenomenology
20 pages latex, no figures. Version-2 includes m->m^2 results, removes Appendix on K-matrix, adds more refs
Scientific paper
10.1016/j.physletb.2005.09.009
We examine the possibility that the form of the lepton mixing matrix can be determined by extremising the Jarlskog flavour invariants associated, eg. with the commutator ($C$) of the lepton mass matrices. Introducing a strictly covariant approach, keeping masses fixed and extremising the determinant (Tr $C^3/3$) leads to maximal CP violation, while extremising the sum of the $2 \times 2$ principal minors ($-{\rm Tr} C^2/2$), 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, eg.\ $|U_{e3}| \simeq \sqrt{2}/3 \sqrt{\Delta m_{12}^2/\Delta m_{23}^2} (1-m_{\mu}/m_{\tau})^2 \simeq 0.07$.
Harrison P. F.
Scott W. G.
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