Abstract
We propose a neutrino mass model with μτ-flavored CP symmetry, where the effective light neutrino Lagrangian enjoys an additional invariance under a Friedberg-Lee (FL) transformation on the left-handed flavor neutrino fields that leads to a highly predictive and testable scenario. While both types of the light neutrino mass ordering, i.e., Normal Ordering (NO) as well as the Inverted Ordering (IO) are allowed, the absolute scale of neutrino masses is fixed by the vanishing determinant of light Majorana neutrino mass matrix Mν. We show that for both types of mass ordering, whilst the atmospheric mixing angle θ23 is in general nonmaximal (θ23 ≠ π/4), the Dirac CP phase δ is exactly maximal (δ = π/2, 3π/2) for IO and nearly maximal for NO owing to cos δ ∝ sin θ13. For the NO, very tiny nonvanishing Majorana CP violation might appear through one of the Majorana phases β; otherwise the model predicts vanishing Majorana CP violation. Thus, despite the fact, that from the measurement of θ23, it is difficult to rule out the model, any large deviation of δ from its maximality, will surely falsify the scenario. For a comprehensive numerical analysis, beside fitting the neutrino oscillation global fit data, we also present a study on the νμ → νe oscillation which is expected to show up Dirac CP violation in different long baseline experiments. Finally, assuming purely astrophysical sources, we calculate the Ultra High Energy (UHE) neutrino flavor flux ratios at neutrino telescopes, such as IceCube, from which statements on the octant of θ23 could be made in our model.
Highlights
We propose a neutrino mass model with μτ -flavored CP symmetry, where the effective light neutrino Lagrangian enjoys an additional invariance under a FriedbergLee (FL) transformation on the left-handed flavor neutrino fields that leads to a highly predictive and testable scenario
For a comprehensive numerical analysis, beside fitting the neutrino oscillation global fit data, we present a study on the νμ → νe oscillation which is expected to show up Dirac CP violation in different long baseline experiments
We propose an invariance of the low energy neutrino Majorana mass term under a mixed μτ -flavored CP symmetry CPμτθ compounded with a generic Friedberg-Lee (FL) transformation on the left-handed flavor neutrino fields
Summary
Using (1.7), a 3 × 3 symmetric mass matrix can most generally be parametrized as:. For simplicity, we restrict to a reasonable choice that ηl are a priori arbitrary complex numbers with same phases, so that the ratios η1 η1. In (2.1), there are five real free parameters: a1, a2, c1, η1 η2 and θ which can be well constrained by existing neutrino oscillation global-fit data. Mν in can be diagonalized by a similarity transformation with a unitary matrix U :. Without any loss of generality, we work in the diagonal basis of the charged lepton so that U can be related to the P M N S mixing matrix UP MNS as c12c13 ei α 2. Where Pφ = diag (eiφ, eiφ, eiφ3) is an unphysical diagonal phase matrix and cij ≡ cos θij, sij ≡ sin θij with the mixing angles θij ∈ [0, π/2]. We work within the PDG convention [69] but denote our Majorana phases by α and β. CP-violation enters through nontrivial values of the Dirac phase δ and of the Majorana phases α, β where δ, α, β ∈ [0, 2π]
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