Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-10-19
Acta Phys.Polon. B36 (2005) 865-880
Physics
High Energy Physics
High Energy Physics - Phenomenology
LaTeX, 1+10 pages. The term "irreducible" applied to the considered doublet representations of the four-group is replaced by t
Scientific paper
Two sets of four 3x3 matrices 1^(3), varphi_1, varphi_2, varphi_3 and 1^(3), mu_1, mu_2, mu_3 are constructed, forming two unitarily isomorphic reducible representations 3 of the group Z_2 x Z_2 called often the four-group. They are related to each other through the effective neutrino mixing matrix U with s_{13} = 0, and generate four discrete transformations of flavor and mass active neutrinos, respectively. If and only if s_{13} = 0, the generic form of effective neutrino mass matrix M becomes invariant under the subgroup Z_2 of Z_2 x Z_2 represented by the matrices 1^(3) and varphi_3. In the approximation of m_1 = m_2, the matrix M becomes invariant under the whole Z_2 x Z_2 represented by the matrices 1^(3), varphi_1, varphi_2, varphi_3. The effective neutrino mixing matrix U with s_{13} = 0 is always invariant under the whole Z_2 x Z_2 represented in two ways, by the matrices 1^(3), varphi_1, varphi_2, varphi_3 and 1^(3), mu_1, mu_2, mu_3.
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