Discrete symmetries, roots of unity, and lepton mixing

Abstract

We investigate the possibility that the first column of the lepton mixing matrix U is given by u_1 = (2,-1,-1)^T/sqrt{6}. In a purely group-theoretical approach, based on residual symmetries in the charged-lepton and neutrino sectors and on a theorem on vanishing sums of roots of unity, we discuss the finite groups which can enforce this. Assuming that there is only one residual symmetry in the Majorana neutrino mass matrix, we find the almost unique solution Z_q x S_4 where the cyclic factor Z_q with q = 1,2,3,... is irrelevant for obtaining u_1 in U. Our discussion also provides a natural mechanism for achieving this goal. Finally, barring vacuum alignment, we realize this mechanism in a class of renormalizable models.

16 pages, no figures. Erroneous theorem 1 replaced by a theorem of Conway and Jones, appendix A extended, conclusions unchanged

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• Precision neutrino experiments vs the Littlest Seesaw
• Neutrino Mixing with Non-Zero ${\theta }_{13}$ and CP Violation in the 3-3-1 Model Based on $S_4$ Flavor Symmetry
• How good is μ-τsymmetry after results on non-zero θ_{13}?
• Residual Z2 x Z2 symmetries and lepton mixing
• Littlest Seesaw model from S4 x U(1)
• Direct and Semi-Direct Approaches to Lepton Mixing with a Massless Neutrino
• Littlest mu-tau seesaw
• Lepton mass and mixing in a Neutrino Mass Model based on $S_4$ flavor symmetry
• A modified Friedberg-Lee symmetry for the TM1 neutrino mixing
• Lepton Mixing, Residual Symmetries, and Trigonometric Diophantine Equations
• Double seesaw mechanism and lepton mixing
• Low scale leptogenesis and $T{M}_1$ mixing in neutrinophillic two Higgs doublet model($\nu$2HDM) with S4 flavor symmetry
• Resonant leptogenesis and TM${}_1$ mixing in minimal Type-I seesaw model with S${}_4$ symmetry