Pseudo-Dirac neutrinos from flavour dependent CP symmetry

Abstract

Discrete residual symmetries and flavour dependent CP symmetries consistent with them have been used to constrain neutrino mixing angles and CP violating phases. We discuss here role of such CP symmetries in obtaining a pseudo-Dirac neutrino which can provide a pair of neutrinos responsible for the solar splitting. It is shown that if (a) $3\times 3$ Majorana neutrino matrix $M_{\nu }$ is invariant under a discrete $Z_2\times Z_2$ symmetry generated by $S_{1,2}$, (b) CP symmetry $X$ transform $M_{\nu }$ as $X^T{M}_{\nu }X=M_{\nu }^{\ast }$, and (c) $X$ and $S_{1,2}$ obey consistency conditions $X{S}_{1,2}^{\ast }{X}^{†}=S_{2,1}$, then two of the neutrino masses are degenerate independent of specific forms of $X$, $S_1$ and $S_2$. Explicit examples of this result are discussed in the context of $\Delta (6n^2)$ groups which can also be used to constrain neutrino mixing matrix $U$. Degeneracy in two of the masses does not allow complete determination of $U$ but it can also be fixed once the perturbations are introduced. We consider explicit perturbations which break $Z_2\times Z_2$ symmetries but respect CP. These are shown to remove the degeneracy and provide a predictive description of neutrino spectrum. In particular, a correlation $\sin 2{\theta }_{23}\sin {\delta }_{CP}=\pm \mathrm{Im}[p]$ is obtained between the atmospheric mixing angle ${\theta }_{23}$ and the CP violating phase ${\delta }_{CP}$ in terms of a group theoretically determined phase factor $p$. Experimentally interesting case ${\theta }_{23}=\frac{\pi }{4}$, ${\delta }_{CP}=\pm \frac{\pi }{2}$ emerges for groups which predict purely imaginary $p$. We present detailed predictions of the allowed ranges of neutrino mixing angles, phases and the lightest neutrino mass for three of the lowest $\Delta (6n^2)$ groups with $n=2,4,6$.

arXiv comment17 pages, 4 figures; Minor modification, published version

References in corpus (26)

• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• Neutrino Mass and Mixing with Discrete Symmetry
• Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity
• A non-standard CP transformation leading to maximal atmospheric neutrino mixing
• The Horizontal Symmetry for Neutrino Mixing
• CP and Discrete Flavour Symmetries
• A review of mu-tau flavor symmetry in neutrino physics
• Symmetry of Lepton Mixing
• CP Violation from Finite Groups
• The Flavor Group Delta(6n^2)
• Lepton Mixing Predictions from Delta(6n^2) Family Symmetry
• μ-τSymmetry and Maximal CP Violation
• Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP
• Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries
• 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
• Generalized $\mu -\tau$ reflection symmetry and leptonic CP violation
• Cosmological constraints on the neutrino mass including systematic uncertainties
• Generalized $\mu$-$\tau$ symmetry and discrete subgroups of O(3)
• Leptonic Dirac CP Violation Predictions from Residual Discrete Symmetries
• Leptonic CP violation: zero, maximal or between the two extremes
• Origin of Constrained Maximal CP Violation in Flavor Symmetry
• Lepton Mixing Predictions from Infinite Group Series $D_{9n,3n}^{(1)}$ with Generalized CP
• Discrete symmetries and models of flavor mixing
• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$

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