Tri-Direct CP in the Littlest Seesaw Playground

TL;DR

This paper introduces a novel tri-direct CP approach in neutrino models, utilizing multiple residual symmetries to better predict neutrino parameters, and proposes new variants of the Littlest Seesaw model with specific vacuum alignments.

Contribution

It develops a new tri-direct CP framework with multiple residual symmetries and applies it to create and analyze new Littlest Seesaw model variants.

Findings

New variants of Littlest Seesaw with distinct predictions.

Numerical analysis of model predictions.

Explicit model realization with specific flavon alignments.

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 $(1, -7/2, -7/2 )$.