2004/10/25 by Wojciech Krolikowski
Physics and Astronomy · #hep-ph
published as Acta Phys.Polon. B36 (2005) 865-880 · LaTeX, 1+10 pages. The term "irreducible" applied to the considered doublet representations of the four-group is replaced by the correct term "not reduced"
arxiv created 2004/10/25 · arxiv updated 2009/12/01
Two sets of four 3x3 matrices 1^(3), varphi1, varphi2, varphi3 and 1^(3), mu1, mu2, mu3 are constructed, forming two unitarily isomorphic reducible representations 3 of the group Z2 x Z2 called often the four-group. They are related to each other through the effective neutrino mixing matrix U with s13 = 0, and generate four discrete transformations of flavor and mass active neutrinos, respectively. If and only if s13 = 0, the generic form of effective neutrino mass matrix M becomes invariant under the subgroup Z2 of Z2 x Z2 represented by the matrices 1^(3) and varphi3. In the approximation of m1 = m2, the matrix M becomes invariant under the whole Z2 x Z2 represented by the matrices 1^(3), varphi1, varphi2, varphi3. The effective neutrino mixing matrix U with s13 = 0 is always invariant under the whole Z2 x Z2 represented in two ways, by the matrices 1^(3), varphi1, varphi2, varphi3 and 1^(3), mu1, mu2, mu3.