# Trimaximal neutrino mixing from vacuum alignment in *A* _{4} and *S* _{4} models

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## Abstract

Recent T2K results indicate a sizeable reactor angle *θ* _{13} which would rule out *exact* tri-bimaximal lepton mixing. We study the vacuum alignment of the Altarelli-Feruglio *A* _{4} family symmetry model including additional flavons in the **1′** and **1″** representations and show that it leads to trimaximal mixing in which the second column of the lepton mixing matrix consists of the column vector \( {{{{{\left( {1,1,1} \right)}^T}}} \left/ {{\sqrt {3} }} \right.} \), with a potentially large reactor angle. In order to limit the reactor angle and control the higher order corrections, we propose a renormalisable *S* _{4} model in which the **1′** and **1″** flavons of *A* _{4} are unified into a doublet of *S* _{4} which is spontaneously broken to *A* _{4} by a flavon which enters the neutrino sector at higher order. We study the vacuum alignment in the *S* _{4} model and show that it predicts *accurate* trimaximal mixing with *approximate* tri-bimaximal mixing, leading to a new mixing sum rule testable in future neutrino experiments. Both *A* _{4} and *S* _{4} models preserve form dominance and hence predict zero leptogenesis, up to renormalisation group corrections.

## Keywords

Neutrino Physics Discrete and Finite Symmetries Beyond Standard Model## References

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