Residual Z2 X Z2 symmetries and lepton mixing

We consider two novel scenarios of residual symmetries of the lepton mass matrices. Firstly we assume a Z(2) X Z(2) symmetry G(l) for the charged-lepton mass matrix and a Z(2) symmetry G(v) for the light neutrino mass matrix. With this setting, the moduli of the elements of one column of the lepton mixing matrix are fixed up to a reordering. One may interchange the roles of G(l) and G(v) in this scenario, thereby constraining a row, instead of a column, of the mixing matrix. Secondly we assume a residual symmetry group G(l congruent to) Zm (m>2) which is generated by a matrix with a doubly-degenerate eigenvalue. Then, with G congruent to Z(2) X Z(2) the moduli of the elements of a row of the lepton mixing matrix get fixed. Using the library of small groups we have performed a search for groups which may embed G(l) and G(v) in each of these two scenarios. We have found only two phenomenologically viable possibilities, one of them constraining a column and the other one a row of the mixing matrix. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license