2003/04/28 by W. Krolikowski
Physics and Astronomy · #hep-ph
published as Acta Phys.Polon. B34 (2003) 4157-4166 · 1+9 pages, latex, no figures
arxiv created 2003/04/28 · arxiv updated 2009/11/30
We observe that the \it invariance of neutrino mixing matrix under the simultaneous discrete transformations ν1, ν2, ν3 → -ν1, -ν2, ν3 and νe, νμ, ντ→ -νe, ντ, νμ (neutrino "horizontal conjugation") \it characterizes (as a sufficient condition for it) the familiar bilarge form of neutrino mixing matrix, favored experimentally at present. Thus, the mass neutrinos ν1, ν2, ν3 get a new quantum number, \it covariant with respect to their mixings into the flavor neutrinos νe, νμ, ντ (neutrino "horizontal parity" equal to -1, -1,1, respectively). The "horizontal parity" turns out to be embedded in a group structure consisting of some Hermitian and real 3× 3 matrices μ1, μ2, μ3 and ϕ1, ϕ2, ϕ3 , forming pairs interconnected through neutrino mixings. They generate some discrete transformations of mass and flavor neutrinos, respectively, in such a way that the group relations μ1 μ2 = μ3 (cyclic) and ϕ1 ϕ2 = ϕ3 (cyclic) hold, while μa μb = μb μa and ϕa ϕb = ϕb ϕa . Then, for instance, the μ3 matrix may be chosen equal to the "horizontal parity".