Leptonic Dirac CP Violation Predictions from Residual Discrete Symmetries

Abstract

Assuming that the observed pattern of 3-neutrino mixing is related to the existence of a (lepton) flavour symmetry, corresponding to a non-Abelian discrete symmetry group $G_f$, and that $G_f$ is broken to specific residual symmetries $G_e$ and $G_{\nu }$ of the charged lepton and neutrino mass terms, we derive sum rules for the cosine of the Dirac phase $\delta$ of the neutrino mixing matrix $U$. The residual symmetries considered are: i) $G_e=Z_2$ and $G_{\nu }=Z_n$, $n>2$ or $Z_n\times Z_m$, $n,m\ge 2$; ii) $G_e=Z_n$, $n>2$ or $Z_n\times Z_m$, $n,m\ge 2$ and $G_{\nu }=Z_2$; iii) $G_e=Z_2$ and $G_{\nu }=Z_2$; iv) $G_e$ is fully broken and $G_{\nu }=Z_n$, $n>2$ or $Z_n\times Z_m$, $n,m\ge 2$; and v) $G_e=Z_n$, $n>2$ or $Z_n\times Z_m$, $n,m\ge 2$ and $G_{\nu }$ is fully broken. For given $G_e$ and $G_{\nu }$, the sum rules for $\cos \delta$ thus derived are exact, within the approach employed, and are valid, in particular, for any $G_f$ containing $G_e$ and $G_{\nu }$ as subgroups. We identify the cases when the value of $\cos \delta$ cannot be determined, or cannot be uniquely determined, without making additional assumptions on unconstrained parameters. In a large class of cases considered the value of $\cos \delta$ can be unambiguously predicted once the flavour symmetry $G_f$ is fixed. We present predictions for $\cos \delta$ in these cases for the flavour symmetry groups $G_f=S_4$, $A_4$, $T^{\prime }$ and $A_5$, requiring that the measured values of the 3-neutrino mixing parameters ${\sin }^2{\theta }_{12}$, ${\sin }^2{\theta }_{13}$ and ${\sin }^2{\theta }_{23}$, taking into account their respective $3\sigma$ uncertainties, are successfully reproduced.

62 pages, includes 6 figures and 14 tables; results unchanged; sections 7 and 8 revised; typos corrected; matches published version

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• Assessing the Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries for Description of Neutrino Mixing
• CP Violation in the Lepton Sector and Implications for Leptogenesis
• Predictions for the Majorana CP Violation Phases in the Neutrino Mixing Matrix and Neutrinoless Double Beta Decay
• Alternative Schemes of Predicting Lepton Mixing Parameters from Discrete Flavor and CP Symmetry
• Generalized CP and $\Delta (3n^2)$ Family Symmetry for Semi-Direct Predictions of the PMNS Matrix
• Combining texture zeros with a remnant CP symmetry in the minimal type-I seesaw
• Revisiting Minimal Lepton Flavour Violation in the Light of Leptonic CP Violation
• Neutrino Mixing and Leptonic CP Violation from $S_4$ Flavour and Generalised CP Symmetries
• Towards the minimal seesaw model via CP violation of neutrinos
• Stitching an Asymmetric Texture with ${\mathcal{T}}_{13}\times {\mathcal{Z}}_5$ Family Symmetry
• Mu-tau reflection symmetry with a high scale texture-zero
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
• Addressing Neutrino Mixing Models with DUNE and T2HK
• Renormalisation Group Corrections to Neutrino Mass Sum Rules
• Lepton Sector Phases and Their Roles in Flavor and Generalized CP Symmetries
• Predictivity of Neutrino Mass Sum Rules
• A Survey of Neutrino Flavor Models and the Neutrinoless Double Beta Decay Funnel
• Neutrino CP violation and sign of baryon asymmetry in the minimal seesaw model
• Renormalisation Group Corrections to Neutrino Mixing Sum Rules
• Leptonic Sum Rules from Flavour Models with Modular Symmetries
• Probing Lepton Flavor Models at Future Neutrino Experiments
• Testing Lepton Flavor Models at ESSnuSB
• Tribimaximal Mixing in the $SU(5)\times {\mathcal{T}}_{13}$ Texture
• A hybrid setup for fundamental unknowns in neutrino oscillations using T2HK ($\nu$) and $\mu$-DAR ($\bar{\nu }$)
• Predictions for the Dirac CP-Violating Phase from Sum Rules
• Importance of generalized $\mu \tau$ symmetry and its CP extension on neutrino mixing and leptogenesis
• Radiative Corrections to the Solar Lepton Mixing Sum Rule
• Neutrino non-standard interactions as a portal to test flavour symmetries
• Neutrino Mass Sum Rules and Symmetries of the Mass Matrix
• Confronting the prediction of leptonic Dirac CP-violating phase with experiments
• Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?
• Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries in Light of the First JUNO Result
• Pseudo-Dirac neutrinos from flavour dependent CP symmetry
• An $S_4$ model inspired from self-complementary neutrino mixing
• Predictions for the Leptonic Dirac CP-Violating Phase
• Octant of ${\theta }_{23}$, MH, $0\nu \beta \beta$ decay and vacuum alignment of $A_4$ flavour symmetry in an inverse seesaw model
• The Minimal Flavor Structure from Decomposition of the Fermion Mass Matrix
• CP-like Symmetry with Discrete and Continuous Groups and CP Violation/Restoration
• Exploring dynamics of $A_4$ flavour symmetry using low scale seesaw mechanisms