Alternative Schemes of Predicting Lepton Mixing Parameters from Discrete Flavor and CP Symmetry

Abstract

We suggest two alternative schemes to predict lepton mixing angles as well as $CP$ violating phases from a discrete flavor symmetry group combined with $CP$ symmetry. In the first scenario, the flavor and $CP$ symmetry is broken to the residual groups of the structure $Z_2\times CP$ in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters ${\theta }_{\nu }$ and ${\theta }_l$. This type of breaking pattern is extended to the quark sector. In the second scheme, an abelian subgroup contained in the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant $CP$ transformation, all lepton mixing parameter are determined in terms of three free parameters ${\theta }_{1,2,3}$. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters ${\theta }_{\nu ,l}$ and ${\theta }_{1,2,3}$ is taken into account. We have studied the lepton mixing patterns arising from the flavor group $S_4$ and $CP$ symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.

47 pages, 12 figures

References in corpus (23)

• Observation of electron-antineutrino disappearance at Daya Bay
• Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Neutrino oscillations refitted
• Search for Neutrinoless Double-Beta Decay in ${}^{136}$Xe with EXO-200
• Limit on Neutrinoless ββ Decay of Xe-136 from the First Phase of KamLAND-Zen and Comparison with the Positive Claim in Ge-76
• Improved Measurement of Electron Antineutrino Disappearance at Daya Bay
• Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with 6.6E20 protons on target
• S_4 Flavored CP Symmetry for Neutrinos
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP
• Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons
• Lepton Mixing Predictions including Majorana Phases from $\Delta (6n^2)$ Flavour Symmetry and Generalised CP
• Rephasing Invariants of Quark and Lepton Mixing Matrices
• Lepton Mixing Parameters from $\Delta (48)$ Family Symmetry and Generalised CP
• A Long Baseline Neutrino Oscillation Experiment Using J-PARC Neutrino Beam and Hyper-Kamiokande
• Classification of lepton mixing matrices from finite residual symmetries
• Generalised CP and $\Delta (96)$ Family Symmetry
• Lepton Flavor Mixing and CP Symmetry
• A Bottom-Up Approach to Lepton Flavor and CP Symmetries
• $A_4$ and CP symmetry and a model with maximal CP violation
• [Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
• New results from RENO and prospects with RENO-50

Cited by in corpus (3)

• The symmetry approach to quark and lepton masses and mixing
• Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP
• Dihedral flavor group as the key to understand quark and lepton flavor mixing