Charged Lepton Corrections to Neutrino Mixing Angles and CP Phases Revisited

Abstract

We re-analyze charged lepton corrections to neutrino mixing angles and CP phases, carefully including CP phases from the charged lepton sector. We present simple analytical formulae for including the charged lepton corrections and derive compact new results for small neutrino and charged lepton mixings ${\theta }_{13}^{\nu }$ and ${\theta }_{13}^e$. We find a generic relation ${\theta }_{12}+\frac{1}{\sqrt{2}}{\theta }_{12}^e\cos (\delta -\pi )\approx {\theta }_{12}^{\nu }$, which relates the prediction from the neutrino sector ${\theta }_{12}^{\nu }$ to the charged lepton mixing ${\theta }_{12}^e$ and to the MNS neutrino oscillation phase $\delta$. We apply our formula to the examples of bimaximal or tri-bimaximal neutrino mixing. One implication is that the so-called quark-lepton complementarity relation ${\theta }_{12}+{\theta }_C=45^{\circ }$ can only hold for $\delta =\pi$ and it gets modified in the presence of leptonic CP violation. On the other hand, the lepton mixing ${\theta }_{13}$ generated from the charged lepton correction ${\theta }_{12}^e$ is independent of CP phases and given by ${\theta }_{13}=\frac{1}{\sqrt{2}}{\theta }_{12}^e$. Combining these results leads to a model-independent sum rule: ${\theta }_{12}+{\theta }_{13}\cos (\delta -\pi )\approx {\theta }_{12}^{\nu }$ where ${\theta }_{12}^{\nu }=(35.26^{\circ })45^{\circ }$ in the case of (tri-)bimaximal neutrino mixing, for example.

10 pages, references added and minor changes in the text

References in corpus (11)

• Running Neutrino Mass Parameters in See-Saw Scenarios
• Cabibbo Haze in Lepton Mixing
• Quark-Lepton Complementarity in Unified Theories
• Nontrivial Correlation between the CKM and MNS Matrices
• QLC relation and neutrino mass hierarchy
• Importance of Threshold Corrections in Quark-Lepton Complementarity
• Unified Parametrization of Quark and Lepton Mixing Matrices
• Screening of Dirac flavor structure in the seesaw and neutrino mixing
• Lepton Flavor Violation as a Probe of Quark-Lepton Unification
• Bimaximal fermion mixing from the quark and leptonic mixing matrices
• Models of Neutrino Masses and Mixings

Cited by in corpus (148)

• Neutrino Mass and Mixing with Discrete Symmetry
• Neutrino Mass and Mixing: from Theory to Experiment
• Flavour physics of leptons and dipole moments
• Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry
• Physics at a future Neutrino Factory and super-beam facility
• Unified Models of Neutrinos, Flavour and CP Violation
• CKM and Tri-bimaximal MNS Matrices in a SU(5) x (d)T Model
• A4 family symmetry and quark-lepton unification
• A review of mu-tau flavor symmetry in neutrino physics
• Comparing Trimaximal Mixing and Its Variants with Deviations from Tri-bimaximal Mixing
• A predictive A4 model, Charged Lepton Hierarchy and Tri-bimaximal Sum Rule
• A4 See-Saw Models and Form Dominance
• Parametrizing the lepton mixing matrix in terms of deviations from tri-bimaximal mixing
• Flavour-Dependent Leptogenesis with Sequential Dominance
• A SUSY GUT of Flavour with S4 x SU(5) to NLO
• Sizeable θ_13 from the Charged Lepton Sector in SU(5), (Tri-)Bimaximal Neutrino Mixing and Dirac CP Violation
• New GUT predictions for quark and lepton mass ratios confronted with phenomenology
• On the origin of neutrino flavour symmetry
• Tri-bimaximal-Cabibbo Mixing
• Group Theoretical Origin of CP Violation
• Determining the Dirac CP Violation Phase in the Neutrino Mixing Matrix from Sum Rules
• Towards a Complete Theory of Fermion Masses and Mixings with SO(3) Family Symmetry and 5d SO(10) Unification
• Predicting the Values of the Leptonic CP Violation Phases
• TriMinimal Parametrization of the Neutrino Mixing Matrix
• $A_4$ Family Symmetry from SU(5) SUSY GUTs in 6d
• Mixing angle and phase correlations from A5 with generalised CP and their prospects for discovery
• Neutrino Mixing Sum Rules and Oscillation Experiments
• U_{PMNS} = U_ell^dagger U_nu
• Systematic uncertainties in long-baseline neutrino oscillations for large ${\theta }_{13}$
• Large neutrino mixing angle θ_{13}^{MNS} and quark-lepton mass ratios in unified flavour models
• Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification
• A Supersymmetric Grand Unified Theory of Flavour with PSL(2,7) x SO(10)
• Quark lepton complementarity and renormalization group effects
• Nonzero |U_e3| from Charged Lepton Corrections and the Atmospheric Neutrino Mixing Angle
• An SO(10)XS4 Model of Quark-Lepton Complementarity
• Generalised Geometrical CP Violation in a $T^{\prime }$ Lepton Flavour Model
• Deviations from Tri-bimaximal Mixing: Charged Lepton Corrections and Renormalization Group Running
• θ^PMNS_13 = θ_C / \sqrt2 from GUTs
• Fermionic Dark Matter in Radiative Inverse Seesaw Model with U(1)_{B-L}
• Solving the SUSY Flavour and CP Problems with SU(3) Family Symmetry
• Tri-bimaximal Neutrino Mixing and ${\theta }_{13}$
• Leptonic CP violation: zero, maximal or between the two extremes
• The Seesaw Mechanism in Quark-Lepton Complementarity
• The Power of Neutrino Mass Sum Rules for Neutrinoless Double Beta Decay Experiments
• A4xSU(5) SUSY GUT of Flavour with Trimaximal Neutrino Mixing
• Large U_{e3} and Tri-bimaximal Mixing
• A_4xSU(5) SUSY GUT of Flavour in 8d
• Testing atmospheric mixing sum rules at precision neutrino facilities
• Third Family Corrections to Quark and Lepton Mixing in SUSY Models with non-Abelian Family Symmetry
• Predictions for the Leptonic Dirac CP Violation Phase: a Systematic Phenomenological Analysis
• Neutrino Masses and Mixings from String Theory Instantons
• Low and High Energy Phenomenology of Quark-Lepton Complementarity Scenarios
• A flavour GUT model with theta_13^PMNS = theta_C / sqrt(2)
• Testing solar lepton mixing sum rules in neutrino oscillation experiments
• Spontaneous CP violation in A4xSU(5) with Constrained Sequential Dominance 2
• Viewing Lepton Mixing through the Cabibbo Haze
• An SU(5) x A5 Golden Ratio Flavour Model
• Third Family Corrections to Tri-bimaximal Lepton Mixing and a New Sum Rule
• SUSY S4 x SU(5) revisited
• Adjoint SUSY $SU(5)$ Grand Unified Model with $S_4$ Flavor Symmetry
• A New Type of Complex Neutrino Mass Texture and mu-tau Symmetry
• Systematic Parameter Space Search of Extended Quark-Lepton Complementarity
• Perturbative Estimates of Lepton Mixing Angles in Unified Models
• Group space scan of flavor symmetries for nearly tribimaximal lepton mixing
• Parametrizing the Lepton Mixing Matrix in terms of Charged Lepton Corrections
• Measurable Neutrino Mass Scale in A4 x SU(5)
• [Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
• SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry
• The symmetry approach to quark and lepton masses and mixing
• Flavored Orbifold GUT - an SO(10) x S4 model
• Quark mixing sum rules and the right unitarity triangle
• Discrete Symmetries and Neutrino Mass Perturbations for θ_{13}
• Quantum numbers of heavy neutrinos, tri-bi-maximal mixing through double seesaw with permutation symmetry, and comment on ${\theta }_{\mathrm{sol}}+{\theta }_c\simeq \frac{\pi }{4}$
• Invariant see-saw models and sequential dominance
• A new relation between quark and lepton mixing matrices
• Leptogenesis in an SU(5) x A5 Golden Ratio Flavour Model
• Spontaneous breaking of $SO(3)$ to finite family symmetries with supersymmetry - an $A_4$ model
• Matter inflation with A_4 flavour symmetry breaking
• Model-Independent Analysis of Tri-bimaximal Mixing -- a Softly-Broken Hidden or an Accidental Symmetry?
• Inverse neutrino mass hierarchy in a flavour GUT model
• Renormalisation Group Corrections to Neutrino Mass Sum Rules
• Corrections for tribimaximal, bimaximal and democratic neutrino mixing matrices
• Suppressed FCNC in New Physics with Shared Flavor Symmetry
• Neutrino Mixing Angles in Sequential Dominance to NLO and NNLO
• Vacuum misalignment corrections to tri-bimaximal mixing and form dominance
• Deviation from tri-bimaximal mixings in two types of inverted hierarchical neutrino mass models
• Charged lepton contributions to bimaximal and tri-bimaximal mixings for generating $\sin {\theta }_{13}\ne 0$ and ${\tan }^2{\theta }_{23}<1$
• Prediction of Leptonic CP Phase in $A_4$ symmetric model
• ${\theta }_{13}^{}$ and The Flavor Ring
• Predictivity of Neutrino Mass Sum Rules
• From Flavour to SUSY Flavour Models
• Modifications to the neutrino mixing from the mu-tau reflection symmetry
• Non-universal Z' from SO(10) GUTs with vector-like family and the origin of neutrino masses
• Lepton Flavour Violation in the Constrained MSSM with Constrained Sequential Dominance
• Predicting Leptonic CP phase by considering deviations in charged lepton and neutrino sectors
• Prediction of leptonic CP phase from perturbatively modified tribimaximal (or bimaximal) mixing
• Mu-Tau Reflection Symmetry in the Standard Parametrization and Contributions from Charged Lepton Sector
• Neutrino mixing in SO(10) GUTs with non-abelian flavor symmetry in the hidden sector
• Charged Lepton Corrections to Scaling Neutrino Mixing
• Perturbing exactly tri-bimaximal neutrino mixings with charged lepton mass matrices
• Testing Lepton Flavor Models at ESSnuSB
• Quasi-degenerate neutrinos and tri-bi-maximal mixing
• Models for Neutrino Masses and Mixings
• Deviation from Tri-Bimaximal Mixing and Large Reactor Mixing Angle
• Quark-Lepton universality and large leptonic mixing
• Stable fermion mass matrices and the charged lepton contribution to neutrino mixing
• Renormalization Group Evolution of Neutrino Parameters in Presence of Seesaw Threshold Effects and Majorana Phases
• Consistency of perturbed Tribimaximal, Bimaximal and Democratic mixing with Neutrino mixing data
• Can an unbroken flavour symmetry provide an approximate description of lepton masses and mixing?
• Quasi-degenerate neutrinos and tri-bi-maximal mixing
• Predictions for the Dirac CP-Violating Phase from Sum Rules
• Neutrino Mass Models: circa 2008
• Entangled maximal mixings in U_PMNS=U_l^dagger U_nu, and a connection to complex mass textures
• Patterns in the Fermion Mixing Matrix, a bottom-up approach
• Neutrino phenomenology in the flavored NMSSM without domain wall problems
• Reducing θ_13 to 9 degrees
• Deviations from tri-bimaximal mixing
• Radiative Corrections to the Solar Lepton Mixing Sum Rule
• Large Lepton Mixings from Continuous Symmetries
• Neutrino Mass and Flavour Models
• Lepton mixing from the hidden sector
• Family symmetries and the origin of fermion masses and mixings
• A neutrino mass-mixing sum rule from SO(10) and neutrinoless double beta decay
• Lowering solar mixing angle in inverted hierarchy without charged lepton corrections
• Predicting ${\delta }^{\text{PMNS}}$, ${\theta }_{23}^{\text{PMNS}}$ and fermion mass ratios from flavour GUTs with CSD2
• Neutrino mixing sum rules and the Littlest Seesaw
• Exponential parameterization of the neutrino mixing matrix - comparative analysis with different data sets and CP violation
• Neutrino Mass Models: a road map
• Form Invariance and Symmetry in the Neutrino Mass Matrix
• Leptonic CP Violation Phases, Quark-Lepton Similarity and Seesaw Mechanism
• Model independent Analysis of Dirac CP Violating Phase for some well known mixing scenarios
• (Z_2)^3 Symmetry of the Tripartite Model
• Predictions for the Leptonic Dirac CP-Violating Phase
• Revisiting the Quark-Lepton Complementarity and Triminimal Parametrization of Neutrino Mixing Matrix
• CP violating phase from charged-lepton mixing
• SUSY SU(5) $\times S_4$ GUT Flavor Model for Fermion Masses and Mixings with Adjoint, Large ${\theta }_{13}^{PMNS}$
• Quasi-degenerate Neutrino mass models and their significance: A model independent investigation
• Modulated bimaximal neutrino mixing
• Implications of the Zero 1-3 Flavour Mixing Hypothesis: Predictions for ${\theta }_{23}^{\mathrm{PMNS}}$ and ${\delta }^{\mathrm{PMNS}}$
• Neutrino mixing and masses in SO(10) GUTs with hidden sector and flavor symmetries
• A Systematic Analysis of Perturbations for Hexagonal Mixing Matrix
• Neutrino Mass Models: Impact of non-zero reactor angle
• Natural neutrino mass hierarchy in a theory of gauge flavour deconstruction
• Deviation from Tri-Bimaximal Neutrino mixing from the Charged Lepton Sector
• Double Froggatt--Nielsen Mechanism
• Parametrization of lepton mixing matrix in terms of deviations from bi-maximal and tri-bimaximl mixing
• New Parametrization of Neutrino Mixing Matrix
• On the ambiguities in the tri-bimaximal mixing matrix and corresponding charged lepton corrections