Trimaximal neutrino mixing from vacuum alignment in A 4 and S 4 models

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.