# Generalised CP and trimaximal TM 1 lepton mixing in ${S}_{4}$ family symmetry

Li, Cai-Chang (Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China) ; Ding, Gui-Jun  (Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China)

13 February 2014

Abstract: We construct two flavor models based on ${S}_{4}$ family symmetry and generalised CP symmetry. In both models, the ${S}_{4}$ family symmetry is broken down to the ${Z}_{2}^{\mathit{SU}}$ subgroup in the neutrino sector, as a consequence, the trimaximal TM 1 lepton mixing is produced. Depending on the free parameters in the flavon potential, the Dirac CP is predicted to be either conserved or maximally broken, and the Majorana CP phases are trivial. The two models differ in the neutrino sector. The flavon fields are involved in the Dirac mass terms at leading order in the first model, and the neutrino mass matrix contains three real parameters such that the absolute neutrino masses are fixed. Nevertheless, the flavon fields enter into the Majorana mass terms at leading order in the second model. The leading order lepton mixing is of the tri-bimaximal form which is broken down to TM 1 by the next to leading order contributions.

Published in: Nuclear Physics B 881 (2014) 206-232