Neutrino Mixing Sum Rules and Oscillation Experiments

Abstract

The neutrino mixing sum rule ${\theta }_{12}-{\theta }_{13}\cos (\delta )\approx {\theta }_{12}^{\nu }$ provides a possibility to explore the structure of the neutrino mass matrix in the presence of charged lepton corrections, since it relates the 1-2 mixing angle from the neutrino mass matrix, ${\theta }_{12}^{\nu }$, to observable parameters of the PMNS mixing matrix. The neutrino mixing sum rule holds if the charged lepton mixing angles are CKM-like, i.e., small and dominated by a 1-2 mixing, and for small 1-3 mixing in the neutrino mass matrix. These conditions hold in a wide class of well motivated flavour models. We apply this sum rule to present oscillation data, and we investigate the prospects of future neutrino facilities for exploring the sum rule by simulating various setups for long-baseline reactor and accelerator experiments. As explicit examples, we use the sum rule to test the hypotheses of tri-bimaximal and bimaximal neutrino mixing, where ${\theta }_{12}^{\nu }$ is predicted by ${\sin }^2({\theta }_{12}^{\nu })=1/3$ or 1/2, respectively, although the neutrino mixing sum rule can be used to test any prediction for ${\theta }_{12}^{\nu }$.

17 pages, 5 figures; referencing clarified

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• θ^PMNS_13 = θ_C / \sqrt2 from GUTs
• Tri-bimaximal Neutrino Mixing and ${\theta }_{13}$
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• Predictions for Leptonic Mixing Angle Correlations and Non-trivial Dirac CP Violation from $A_5$ with Generalised CP Symmetry
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• A_4xSU(5) SUSY GUT of Flavour in 8d
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• Neutrino Masses and Mixings from String Theory Instantons
• A flavour GUT model with theta_13^PMNS = theta_C / sqrt(2)
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• Measurable Neutrino Mass Scale in A4 x SU(5)
• Quark mixing sum rules and the right unitarity triangle
• Discrete Symmetries and Neutrino Mass Perturbations for θ_{13}
• A new relation between quark and lepton mixing matrices
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• Suppressed FCNC in New Physics with Shared Flavor Symmetry
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• Neutrino phenomenology in the flavored NMSSM without domain wall problems
• Radiative Corrections to the Solar Lepton Mixing Sum Rule
• Neutrino mixing sum rules and the Littlest Seesaw
• Predicting ${\delta }^{\text{PMNS}}$, ${\theta }_{23}^{\text{PMNS}}$ and fermion mass ratios from flavour GUTs with CSD2
• Form Invariance and Symmetry in the Neutrino Mass Matrix
• Neutrino Mass Models: a road map
• (Z_2)^3 Symmetry of the Tripartite Model
• Predictions for the Leptonic Dirac CP-Violating Phase
• Quasi-degenerate Neutrino mass models and their significance: A model independent investigation
• Implications of the Zero 1-3 Flavour Mixing Hypothesis: Predictions for ${\theta }_{23}^{\mathrm{PMNS}}$ and ${\delta }^{\mathrm{PMNS}}$