Predicting the Values of the Leptonic CP Violation Phases

Abstract

Using the fact that the neutrino mixing matrix $U=U_e^{†}{U}_{\nu }$, where $U_e$ and $U_{\nu }$ result from the diagonalisation of the charged lepton and neutrino mass matrices, we consider a number of forms of $U_{\nu }$ associated with a variety of flavour symmetries: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding iii) to the conservation of the lepton charge $L^{\prime }=L_e-L_{\mu }-L_{\tau }$ (LC), iv) to golden ratio type A (GRA) mixing, v) golden ratio type B (GRB) mixing, and iii) to hexagonal (HG) mixing. Employing the minimal form of $U_e$ that can provide the requisite corrections to $U_{\nu }$ so that reactor, atmospheric and solar neutrino mixing angles ${\theta }_{13}$, ${\theta }_{23}$ and ${\theta }_{12}$ have values compatible with the current data, including a possible sizable deviation of ${\theta }_{23}$ from $\pi /4$, we discuss the possibility to obtain predictions for the CP violation phases in the neutrino mixing matrix. Following the approach developed in [1] we derive predictions for the Dirac phase $\delta$ and the rephasing invariant $J_{\mathrm{CP}}$ in the cases of GRA, GRB and HG forms of $U_{\nu }$ (results for the TBM and BM (LC) forms were obtained in [1]). We show also that under rather general conditions within the scheme considered the values of the Majorana phases in the PMNS matrix can be predicted for each of the forms of $U_{\nu }$ discussed. We give examples of these predictions and of their implications for neutrinoless double beta decay. In the GRA, GRB and HG cases, as in the TBM one, relatively large CP violation effects in neutrino oscillations are predicted ($|J_{CP}|\sim (0.031-0.034)$). Distinguishing between the TBM, BM (LC), GRA, GRB and HG forms of $U_{\nu }$ requires a measurement of $\cos \delta$ or a relatively high precision measurement of $J_{\mathrm{CP}}$.

30 pages, results unchanged, title modified, text (including the Introduction) streamlined, with exception of a few added references version to be published in Nuclear Physics B

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Cited by in corpus (19)

• Determining the Dirac CP Violation Phase in the Neutrino Mixing Matrix from Sum Rules
• A Bottom-Up Approach to Lepton Flavor and CP Symmetries
• An SU(5) x A5 Golden Ratio Flavour Model
• Lepton Mixing in $A_5$ Family Symmetry and Generalized CP
• Leptogenesis in an SU(5) x A5 Golden Ratio Flavour Model
• Towards the minimal seesaw model via CP violation of neutrinos
• A Survey of Neutrino Flavor Models and the Neutrinoless Double Beta Decay Funnel
• Predictions for the Dirac CP Violation Phase in the Neutrino Mixing Matrix
• Renormalisation Group Corrections to Neutrino Mixing Sum Rules
• Neutrino CP violation and sign of baryon asymmetry in the minimal seesaw model
• Leptonic Sum Rules from Flavour Models with Modular Symmetries
• Perturbation to TBM mixing and its phenomenological implications
• Confronting the prediction of leptonic Dirac CP-violating phase with experiments
• Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries in Light of the First JUNO Result
• Deviations to Tri-Bi-Maximal mixing in the limit of $\mu -\tau$ symmetry
• Restricting Majorana phases in the Tri-Bi-Maximal limit
• Implications of the Zero 1-3 Flavour Mixing Hypothesis: Predictions for ${\theta }_{23}^{\mathrm{PMNS}}$ and ${\delta }^{\mathrm{PMNS}}$
• A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry
• Linking Leptonic CP violation to Quark Unitarity Triangle