Determining the Dirac CP Violation Phase in the Neutrino Mixing Matrix from Sum Rules

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 analyse the sum rules which the Dirac phase $\delta$ present in $U$ satisfies when $U_{\nu }$ has a form dictated by flavour symmetries and $U_e$ has a "minimal" form (in terms of angles and phases it contains) 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. The following symmetry forms are considered: i) tri-bimaximal (TBM), ii) bimaximal (BM) (or corresponding to the conservation of the lepton charge $L^{\prime }=L_e-L_{\mu }-L_{\tau }$ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for $\delta$ in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for $\cos \delta$ proposed in the literature, taking into account also the uncertainties in the measured values of ${\sin }^2{\theta }_{12}$, ${\sin }^2{\theta }_{23}$ and ${\sin }^2{\theta }_{13}$. This allows us, in particular, to assess the accuracy of the predictions for $\cos \delta$ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3$\sigma$ experimentally allowed ranges.

arXiv comment37 pages, includes 18 figures and 10 tables; results in v.4 unchanged; typos corrected; matches published version.

References in corpus (60)

• Big-Bang Nucleosynthesis
• Tri-Bimaximal Mixing and the Neutrino Oscillation Data
• Neutrino Mass and Mixing with Discrete Symmetry
• Symmetries and Generalisations of Tri-Bimaximal Neutrino Mixing
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Nearly Tri-Bimaximal Neutrino Mixing and CP Violation
• Neutrino-less Double Beta Decay and Particle Physics
• Status of three-neutrino oscillation parameters, circa 2013
• Bi-Maximal Mixing of Three Neutrinos
• Renormalization of the Neutrino Mass Operator
• Neutrino Mass and Mixing: from Theory to Experiment
• Running Neutrino Masses, Mixings and CP Phases: Analytical Results and Phenomenological Consequences
• Some Simple Mixing and Mass Matrices for Neutrinos
• Renormalization Group Equations for Seesaw Neutrino Masses
• Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification
• Possible Alternatives to Tri-bimaximal Mixing
• The Solar Neutrino Puzzle: An Oscillation Solution with Maximal Neutrino Mixing
• General RG Equations for Physical Neutrino Parameters and their Phenomenological Implications
• Leptogenesis and Low Energy CP Violation in Neutrino Physics
• Majorana Neutrinos, Neutrino Mass Spectrum, CP-Violation and Neutrinoless Double Beta-Decay: I. The Three-Neutrino Mixing Case
• Charged Lepton Corrections to Neutrino Mixing Angles and CP Phases Revisited
• Connecting Low Energy Leptonic CP-violation to Leptogenesis
• Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing
• On Deviations from Bimaximal Neutrino Mixing
• The golden ratio prediction for the solar neutrino mixing
• Discrete Flavour Groups, θ_13 and Lepton Flavour Violation
• Sizeable θ_13 from the Charged Lepton Sector in SU(5), (Tri-)Bimaximal Neutrino Mixing and Dirac CP Violation
• Lepton Mixing Predictions from Delta(6n^2) Family Symmetry
• Unified Parametrization for Quark and Lepton Mixing Angles
• Trimaximal TM1 neutrino mixing in S4 with spontaneous CP violation
• A Maximal Atmospheric Mixing from a Maximal CP Violating Phase
• Can Neutrino Mixings Arise from the Charged Lepton Sector?
• Golden Ratio Prediction for Solar Neutrino Mixing
• Group Theoretical Origin of CP Violation
• Predicting the Values of the Leptonic CP Violation Phases
• Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP
• Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries
• Deviation of Neutrino Mixing from Bi-maximal
• U_{PMNS} = U_ell^dagger U_nu
• Large neutrino mixing angle θ_{13}^{MNS} and quark-lepton mass ratios in unified flavour models
• Model Predictions for Neutrino Oscillation Parameters
• Nonzero |U_e3| from Charged Lepton Corrections and the Atmospheric Neutrino Mixing Angle
• Majorana CP-Violating Phases, RG Running of Neutrino Mixing Parameters and Charged Lepton Flavour Violating Decays
• Generalised Geometrical CP Violation in a $T^{\prime }$ Lepton Flavour Model
• θ^PMNS_13 = θ_C / \sqrt2 from GUTs
• A SUSY SU(5)xT' Unified Model of Flavour with large θ_{13}
• Charged lepton contributions to the solar neutrino mixing and theta_13
• Neutrino Mixings and the S4 Discrete Flavour Symmetry
• Deviation from Bimaximal Mixing and Leptonic CP Phases in $S_4$ Family Symmetry and Generalized CP
• An SU(5) x A5 Golden Ratio Flavour Model
• Theoretical Prospects of Neutrinoless Double Beta Decay
• Interplay between Appearance and Disappearance Channels for Precision Measurements of ${\theta }_{23}$ and $\delta$
• Large θ_13 in a SUSY SU(5)xT' Model
• Quark and lepton mixing angles with a dodeca-symmetry
• Predicting CP violation in Deviation from Tri-bimaximal mixing of Neutrinos
• Discrete Symmetries and Neutrino Mass Perturbations for θ_{13}
• Corrections for tribimaximal, bimaximal and democratic neutrino mixing matrices
• The mass-hierarchy and CP-violation discovery reach of the LBNO long-baseline neutrino experiment
• Leptonic CP Violation and Wolfenstein Parametrization for Lepton Mixing
• Mulitbeam GPU Transient Pipeline for the Medicina BEST-2 Array

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• Unified Models of Neutrinos, Flavour and CP Violation
• A review of mu-tau flavor symmetry in neutrino physics
• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
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• Mixing angle and phase correlations from A5 with generalised CP and their prospects for discovery
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• Leptonic Dirac CP Violation Predictions from Residual Discrete Symmetries
• Assessing the Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries for Description of Neutrino Mixing
• Predictions for Leptonic Mixing Angle Correlations and Non-trivial Dirac CP Violation from $A_5$ with Generalised CP Symmetry
• Predictions for the Leptonic Dirac CP Violation Phase: a Systematic Phenomenological Analysis
• A Bottom-Up Approach to Lepton Flavor and CP Symmetries
• CP Violation in the Lepton Sector and Implications for Leptogenesis
• Sensitivities and synergies of DUNE and T2HK
• Predictions for the Majorana CP Violation Phases in the Neutrino Mixing Matrix and Neutrinoless Double Beta Decay
• 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
• Spontaneous breaking of $SO(3)$ to finite family symmetries with supersymmetry - an $A_4$ model
• Leptogenesis in an SU(5) x A5 Golden Ratio Flavour Model
• Stitching an Asymmetric Texture with ${\mathcal{T}}_{13}\times {\mathcal{Z}}_5$ Family Symmetry
• Towards the minimal seesaw model via CP violation of neutrinos
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
• Renormalisation Group Corrections to Neutrino Mass Sum Rules
• Addressing Neutrino Mixing Models with DUNE and T2HK
• The Leptonic CP Phase from T2(H)K and Muon Decay at Rest
• 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
• 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
• Modifications to the neutrino mixing from the mu-tau reflection symmetry
• Models of Neutrino Mass, Mixing and CP Violation
• Lepton flavor violation in the BLMSSM
• Neutrino Predictions from Generalized CP Symmetries of Charged Leptons
• Neutrino mixing in SO(10) GUTs with non-abelian flavor symmetry in the hidden sector
• 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
• Consistency of perturbed Tribimaximal, Bimaximal and Democratic mixing with Neutrino mixing data
• Predictions for the Dirac CP-Violating Phase from Sum Rules
• A hybrid setup for fundamental unknowns in neutrino oscillations using T2HK ($\nu$) and $\mu$-DAR ($\bar{\nu }$)
• Radiative Corrections to the Solar Lepton Mixing Sum Rule
• A neutrino mass-mixing sum rule from SO(10) and neutrinoless double beta decay
• Search for charged lepton flavor violation of vector mesons in BLMSSM model
• Predicting ${\delta }^{\text{PMNS}}$, ${\theta }_{23}^{\text{PMNS}}$ and fermion mass ratios from flavour GUTs with CSD2
• Confronting the prediction of leptonic Dirac CP-violating phase with experiments
• Model independent Analysis of Dirac CP Violating Phase for some well known mixing scenarios
• Further study on the textures of neutrino mass matrix for maximal atmospherical mixing angle and Dirac CP phase
• Predictions for the Leptonic Dirac CP-Violating Phase
• Testing the minimal $S_4$ model of neutrinos with the Dirac and Majorana phases
• Theory Review of Neutrino Models and CP Violation
• Charged lepton flavor violation in extended BLMSSM
• Muon conversion to electron in nuclei within the BLMSSM
• A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry
• A Modern Look at the Oscillation Physics Case for a Neutrino Factory
• A Systematic Analysis of Perturbations for Hexagonal Mixing Matrix
• The mass ratios parametrization
• The Lepton Flavor Changing Decays and One-loop Muon Anomalous Magnetic Moment in the Extended Mirror Twin Higgs Models
• Lepton mixing patterns from combinations of elementary correlations