Parameter symmetries of neutrino oscillations in vacuum, matter, and approximation schemes

Abstract

Expressions for neutrino oscillations contain a high degree of symmetry, but typical forms for the oscillation probabilities mask these symmetries of the oscillation parameters. We elucidate the $2^7$ parameter symmetries of the vacuum parameters and draw connections to the choice of definitions of the parameters as well as interesting degeneracies. We also show that in the presence of matter an \emph{additional} set of $2^7$ parameter symmetries exist of the matter parameters. Due to the complexity of the exact expressions for neutrino oscillations in matter, numerous approximations have been developed; we show that under certain assumptions, approximate expressions have at most $2^6$ additional parameter symmetries of the matter parameters. We also include one parameter symmetry related to the LMA-Dark degeneracy that holds under the assumption of CPT invariance; this adds one additional factor of two to all of the above cases. Explicit, non-trivial examples are given of how physical observables in neutrino oscillations, such as the probabilities, CP violation, the position of the solar and atmospheric resonance, and the effective $\Delta m^2$'s for disappearance probabilities, are invariant under all of the above symmetries. We investigate which of these parameter symmetries apply to numerous approximate expressions in the literature and show that a more careful consideration of symmetries improves the precision of approximations.

arXiv comment18 pages, 1 figure. Minor changes to addressee referees' comments

References in corpus (41)

• Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
• 2020 Global reassessment of the neutrino oscillation picture
• Golden measurements at a neutrino factory
• Analytic Approximations for Three Neutrino Oscillation Parameters and Probabilities in Matter
• Series expansions for three-flavor neutrino oscillation probabilities in matter
• Another possible way to determine the Neutrino Mass Hierarchy
• CP Violation and Matter Effect in Long Baseline Neutrino Oscillation Experiments
• Neutrino Non-Standard Interactions: A Status Report
• Are solar neutrino oscillations robust?
• The Dark Side of the Solar Neutrino Parameter Space
• Exact Formulas and Simple CP dependence of Neutrino Oscillation Probabilities in Matter with Constant Density
• Improved constraints on neutrino mixing from the T2K experiment with $3.13\times 10^{21}$ protons on target
• Determining the Quark Mixing Matrix From CP-Violating Asymmetries
• CP and T Violation in Neutrino Oscillations and Invariance of Jarlskog's Determinant to Matter Effects
• Symmetrical Parametrizations of the Lepton Mixing Matrix
• Compact Perturbative Expressions For Neutrino Oscillations in Matter
• Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra
• Shedding light on LMA-Dark solar neutrino solution by medium baseline reactor experiments: JUNO and RENO-50
• Testing matter effects in propagation of atmospheric and long-baseline neutrinos
• Two modes of searching for new neutrino interactions at MINOS
• Large-Theta(13) Perturbation Theory of Neutrino Oscillation for Long-Baseline Experiments
• Simple and Compact Expressions for Neutrino Oscillation Probabilities in Matter
• Analytical Approximation of the Neutrino Oscillation Matter Effects at large ${\theta }_{13}$
• Neutrino oscillation probabilities through the looking glass
• Eigenvalues: the Rosetta Stone for Neutrino Oscillations in Matter
• CP and T Trajectory Diagrams for a Unified Graphical Representation of Neutrino Oscillations
• What is $\Delta m_{ee}^2$ ?
• Generalized mass ordering degeneracy in neutrino oscillation experiments
• Simple and Precise Factorization of the Jarlskog Invariant for Neutrino Oscillations in Matter
• Rotations Versus Perturbative Expansions for Calculating Neutrino Oscillation Probabilities in Matter
• The Impact of Different Parameterizations on the Interpretation of CP Violation in Neutrino Oscillations
• Parameters' domain in three flavour neutrino oscillations
• Exponential parameterization of neutrino mixing matrix with account for CP-violation data
• Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations
• A Return To Neutrino Normalcy
• Leptonic CP Violation from a New Perspective
• The Effective $\Delta m_{ee}^2$ in Matter
• Fibonacci Fast Convergence for Neutrino Oscillations in Matter
• Parametric enhancement of flavor oscillation in a three-neutrino framework
• Interplay between the factorization of the Jarlskog Invariant and location of the Solar and Atmospheric Resonances for Neutrino Oscillations in Matter
• Symmetry Finder: A method for hunting symmetry in neutrino oscillation

Cited by in corpus (13)

• How to Identify Different New Neutrino Oscillation Physics Scenarios at DUNE
• New reactor data improves robustness of neutrino mass ordering determination
• Solar Neutrinos and the Strongest Oscillation Constraints on Scalar NSI
• Here Comes the Sun: Solar Parameters in Long-Baseline Accelerator Neutrino Oscillations
• Impact of scalar NSI on the neutrino mass ordering sensitivity at DUNE, HK and KNO
• From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes
• Testing New Physics in Oscillations at a Neutrino Factory
• Determining the Density of the Sun with Neutrinos
• Testing the dark side of neutrino oscillations with the solar neutrino fog at Dark Matter experiments
• Comparative study of the 1-2 exchange symmetries in neutrino frameworks with global and local validities
• Individual Neutrino Masses From a Supernova
• Towards First Detection of the Solar MSW Transition With JUNO
• Neutrino Oscillations in the Three Flavor Paradigm