Abstract
We perform an exhaustive analysis of all possible breaking patterns arising from $S_4\rtimes H_{CP}$ in a new {\it tri-direct CP approach} to the minimal seesaw model with two right-handed neutrinos, and construct a realistic flavour model along these lines. According to this approach, separate residual flavour and CP symmetries persist in the charged lepton, `atmospheric' and `solar' right-handed neutrino sectors, i.e. we have {\it three} symmetry sectors rather than the usual two of the {\it semi-direct CP approach} (charged leptons and neutrinos). Following the {\it tri-direct CP approach}, we find twenty-six kinds of independent phenomenologically interesting mixing patterns. Eight of them predict a normal ordering (NO) neutrino mass spectrum and the other eighteen predict an inverted ordering (IO) neutrino mass spectrum. For each phenomenologically interesting mixing pattern, the corresponding predictions for the PMNS matrix, the lepton mixing parameters, the neutrino masses and the effective mass in neutrinoless double beta decay are given in a model independent way. One breaking pattern with NO spectrum and two breaking patterns with IO spectrum corresponds to form dominance. We find that the lepton mixing matrices of three kinds of breaking patterns with NO spectrum and one form dominance breaking pattern with IO spectrum preserve the first column of the tri-bimaximal (TB) mixing matrix, i.e. yield a TM1 mixing matrix.
Highlights
The discovery of neutrino oscillations implied that neutrinos have masses and there is mixing in the lepton sector
When all three lepton mixing angles and the neutrino mass ratio m22=m23 are restricted to their 3σ regions [1], we find that the parameters x, jηj and r should be in the ranges of 1⁄2−6.238; −3.365, 1⁄20.347π; π and [0.154, 0.607], respectively
If we require that all three lepton mixing angles and two mass squared differences lie in their corresponding experimentally preferred 3σ intervals [1], we find that the lepton mixing parameters and the neutrino masses are predicted to be in rather narrow regions, 0.3362 ≤ sin2θ12 ≤ 0.3364; −0.418 ≤ δCP=π ≤ −0.406; 8.240 meV ≤ m2 ≤ 8.950 meV; 0.02254 ≤ sin2θ13 ≤ 0.02280; 0.556 ≤ sin2θ23 ≤ 0.564; 0.263 ≤ β=π ≤ 0.264; 2.690 meV ≤ mee ≤ 2.985 meV; 49.265 meV ≤ m3 ≤ 51.235 meV: ð5:37Þ
Summary
The discovery of neutrino oscillations implied that neutrinos have masses and there is mixing in the lepton sector. From the breaking of A5 flavor symmetry to different residual subgroups in the charged lepton, atmospheric neutrino and solar neutrino sectors, we can obtain the viable golden LS model which predicts the GR1 lepton mixing pattern [26]. An Abelian subgroup Gl is assumed to be preserved by the charged lepton mass matrix and it allows for the distinction of three generations of charged leptons It is the combination of these three residual symmetries that provides a new way of fixing the lepton mixing parameters and neutrino masses in the tridirect CP approach. The analysis of the remaining 13 kinds of breaking patterns with IO is given in Appendix C
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