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