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Covariant Extremisation of Flavour-Symmetric Jarlskog Invariants and the Neutrino Mixing Matrix | | P. F. Harrison
; W. G. Scott
; | | Date: |
31 Jul 2005 | | Journal: | Phys.Lett. B628 (2005) 93 | | Subject: | hep-ph | | Abstract: | 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 $2 imes 2$ principal minors ($-{
m Tr} C^2/2$), 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. $|U_{e3}| simeq sqrt{2}/3 sqrt{Delta m_{12}^2/Delta m_{23}^2} (1-m_{mu}/m_{ au})^2 simeq 0.07$. | | Source: | arXiv, hep-ph/0508012 | | Services: | Forum | Review | PDF | Favorites | |
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