Tri-Direct CP in the Littlest Seesaw Playground

Abstract

We discuss spontaneously broken CP symmetry in two right-handed neutrino models based on the idea of having a {\it different residual flavour symmetry}, together with a {\it different residual CP symmetry}, associated with each of the two right-handed neutrinos. The charged lepton sector also has a {\it different residual flavour symmetry}. In such a {\it tri-direct CP approach}, we show that the combination of the three residual flavour and two residual CP symmetries provides a new way of fixing the parameters. To illustrate the approach, we revisit the Littlest Seesaw (LSS) model based on $S_4$ and then propose new variants which have not so far appeared in the literature, with different predictions for each variant. We analyse numerically the predictions of the new variants, and then propose an explicit model which can realise one of the successful benchmark points, based on the atmospheric flavon vacuum alignment $(1,{\omega }^2,\omega )$ and the solar flavon vacuum alignment $(1,-7/2,-7/2)$.

arXiv comment31 pages, 4 figures

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• Modular $S_4$ and $A_4$ Symmetries and Their Fixed Points: New Predictive Examples of Lepton Mixing
• Multiple modular symmetries as the origin of flavour
• The minimal seesaw and leptogenesis models
• Modular $S_4\times SU(5)$ GUT
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• A New Littlest Seesaw Model
• Neutrino mixing sum rules and the Littlest Seesaw
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• Further study on the textures of neutrino mass matrix for maximal atmospherical mixing angle and Dirac CP phase