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arXiv · 1510.03188

Generalized CP and $Δ(3n^2)$ Family Symmetry for Semi-Direct Predictions of the PMNS Matrix

Gui-Jun Ding·Stephen F. King
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Abstract

The generalized CP transformations can only be consistently defined in the context of $Δ(3n^2)$ lepton symmetry if a certain subset of irreducible representations are present in a model. We perform a comprehensive analysis of the possible automorphisms and the corresponding CP transformations of the $Δ(3n^2)$ group. It is sufficient to only consider three automorphisms if $n$ is not divisible by 3 while additional eight types of CP transformations could be imposed for the case of $n$ divisible by 3. We study the lepton mixing patterns which can be derived from the $Δ(3n^2)$ family symmetry and generalized CP in the semi-direct approach. The PMNS matrix is determined to be the trimaximal pattern for all the possible CP transformations, and it can only take two distinct forms.

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Gui-Jun Ding, Stephen F. King. 2015-10-12. Generalized CP and $Δ(3n^2)$ Family Symmetry for Semi-Direct Predictions of the PMNS Matrix. https://doi.org/10.1103/physrevd.93.025013

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