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The four-group Z2 x Z2 as a discrete invariance group of effective neutrino mass matrix

Wojciech Krolikowski

hep-pharXiv:hep-ph/0410257

Abstract

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.

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