Abstract
We discuss spontaneously broken CP symmetry in two right-handed neutrino models based on the idea of having a different residual flavour symmetry, together with a different residual CP symmetry, associated with each of the two right-handed neutrinos. The charged lepton sector also has a different residual flavour symmetry. In such a 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 S4 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, ω2, ω) and the solar flavon vacuum alignment (1, −7/2, −7/2).
Highlights
Leaving residual symmetries Gν HCν P in the neutrino sector and Gl HCl P in the charged lepton sector, leading to mixing angle and CP phase predictions
Gsol HCsoPl in the sector of the other right-handed neutrino, with the charged lepton sector having a residual flavour symmetry Gl, as illustrated in figure 1. In such a tri-direct CP approach we have shown that the combination of the three residual symmetries provides a new way of fixing the parameters
In particular it can lead to vacuum alignments in the neutrino sector which are uniquely fixed by symmetry, unlike the semi-direct CP approach where not all such vacuum alignments are uniquely fixed
Summary
In a two right-handed neutrino model, the light neutrino masses are generated through the seesaw mechanism, and only two right-handed neutrinos are introduced, denoted here as Nactm and Nscol. In order to predict both neutrino masses and lepton mixing parameters, a non-abelian discrete flavor symmetry Gf and generalized CP symmetry HCP are imposed on the model. We assume the parent symmetry Gf HCP is broken down to Gl, Gatm HCatPm and Gsol HCsoPl in the charged lepton, atmospheric neutrino and solar neutrino sectors, respectively. This paradigm is schematically illustrated, and we call it as tridirect CP approach. The following constrained consistency conditions have to be fulfilled, Xratmρ∗r(giatm)(Xratm)−1 = ρr(gjatm), Xrsolρ∗r(gisol)(Xrsol)−1 = ρr(gjsol), giatm, gjatm ∈ Gatm , gisol, gjsol ∈ Gsol This implies that the mathematical structure of the subgroup comprising the residual flavor and CP symmetries is in general a semi-direct product. The tri-direct CP approach provides new opportunity for model building, it allows us to construct quite predictive neutrino mass models as simple as the LSS model
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