Analytic Approximations for Three Neutrino Oscillation Parameters and Probabilities in Matter

Abstract

The corrections to neutrino mixing parameters in the presence of matter of constant density are calculated systematically as series expansions in terms of the mass hierarchy $\dm{21}/\dm{31}$. The parameter mapping obtained is then used to find simple, but nevertheless accurate formulas for oscillation probabibilities in matter including CP-effects. Expressions with one to one correspondence to the vacuum case are derived, which are valid for neutrino energies above the solar resonance energy. Two applications are given to show that these results are a useful and powerful tool for analytical studies of neutrino beams passing through the Earth mantle or core: First, the ``disentanglement problem'' of matter and CP-effects in the CP-asymmetry is discussed and second, estimations of the statistical sensitivity to the CP-terms of the oscillation probabilities in neutrino factory experiments are presented.

17 pages, 3 figures

Cited by in corpus (184)

• Neutrino Physics with JUNO
• Status of global fits to neutrino oscillations
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Observation of Electron Neutrino Appearance in a Muon Neutrino Beam
• Status of three-neutrino oscillation parameters, circa 2013
• Breaking Eight-fold Degeneracies in Neutrino CP Violation, Mixing, and Mass Hierarchy
• Superbeams versus Neutrino Factories
• Flavor structures of charged fermions and massive neutrinos
• Series expansions for three-flavor neutrino oscillation probabilities in matter
• Leptonic CP violation
• Current unknowns in the three neutrino framework
• A review of mu-tau flavor symmetry in neutrino physics
• Recent Progress in Neutrino Factory and Muon Collider Research within the Muon Collaboration
• Physics Potential of the ICAL detector at the India-based Neutrino Observatory (INO)
• Status of three-neutrino oscillations after the SNO-salt data
• Evidence of Electron Neutrino Appearance in a Muon Neutrino Beam
• On the description of non-unitary neutrino mixing
• Solar neutrino oscillation parameters after first KamLAND results
• Neutrino Factories and the "Magic" Baseline
• Prospects of accelerator and reactor neutrino oscillation experiments for the coming ten years
• New CP Violation in Neutrino Oscillations
• The silver channel at the Neutrino Factory
• Exact Formulas and Simple CP dependence of Neutrino Oscillation Probabilities in Matter with Constant Density
• Reactor Neutrino Experiments Compared to Superbeams
• Neutrino Propagation in Matter
• Very Long Baseline Neutrino Oscillation Experiment for Precise Measurements of Mixing Parameters and CP Violating Effects
• The synergy of the golden and silver channels at the Neutrino Factory
• Superbeams plus Neutrino Factory: the golden path to leptonic CP violation
• Optimization of a neutrino factory oscillation experiment
• Three-Neutrino Mixing after the First Results from K2K and KamLAND
• Mass Hierarchy Determination via future Atmospheric Neutrino Detectors
• Exact Formula of Probability and CP Violation for Neutrino Oscillations in Matter
• Compact Perturbative Expressions For Neutrino Oscillations in Matter
• Probing CP violation signal at DUNE in presence of non-standard neutrino interactions
• Earth Matter Effects at Very Long Baselines and the Neutrino Mass Hierarchy
• Synergies between the first-generation JHF-SK and NuMI superbeam experiments
• A Parametrization for the Neutrino Mixing Matrix
• Neutrino oscillations: the rise of the PMNS paradigm
• Perturbation Theory of Neutrino Oscillation with Nonstandard Neutrino Interactions
• Searching for sterile neutrinos in ice
• New ambiguity in probing CP violation in neutrino oscillations
• Neutrino-nucleus interactions and the determination of oscillation parameters
• Theta_13: phenomenology, present status and prospect
• 1-3 leptonic mixing and the neutrino oscillograms of the Earth
• Getting the best out of T2K and NOvA
• Off--axis Beams and Detector Clusters: Resolving Neutrino Parameter Degeneracies
• How two neutrino superbeam experiments do better than one
• New look at the degeneracies in the neutrino oscillation parameters, and their resolution by T2K, NO$\nu$A and ICAL
• Analytical Approximation of the Neutrino Oscillation Matter Effects at large ${\theta }_{13}$
• Overall Feature of CP dependence for Neutrino Oscillation Probability in Arbitrary Matter Profile
• From parameter space constraints to the precision determination of the leptonic Dirac CP phase
• CP Violation in the Lepton Sector and Implications for Leptogenesis
• Neutrino oscillations at DUNE with improved energy reconstruction
• The role of matter density uncertainties in the analysis of future neutrino factory experiments
• Clone flow analysis for a theory inspired Neutrino Experiment planning
• Octant sensitivity for large theta(13) in atmospheric and long baseline neutrino experiments
• Neutrino oscillation studies with laser-driven beam dump facilities
• Non-standard Hamiltonian effects on neutrino oscillations
• Neutrino oscillation probabilities through the looking glass
• Eigenvalues: the Rosetta Stone for Neutrino Oscillations in Matter
• Super-NOvA: a long-baseline neutrino experiment with two off-axis detectors
• Exploration prospects of a long baseline Beta Beam neutrino experiment with an iron calorimeter detector
• A New Nuclear Reactor Neutrino Experiment to Measure theta 13
• The physics of antineutrinos in DUNE and determination of octant and ${\delta }_{CP}$
• Revisiting quantum decoherence for neutrino oscillations in constant matter density
• The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• Optimization of the Neutrino Factory, revisited
• Evidence for leptonic CP phase from NO$\nu$A, T2K and ICAL: A chronological progression
• Determining the Neutrino Mass Hierarchy and CP Violation in NOvA with a Second Off-Axis Detector
• Physics with a very long neutrino factory baseline
• Neutrino oscillation parameters from MINOS, ICARUS and OPERA combined
• Wolfenstein-like Parametrization of the Neutrino Mixing Matrix
• Long-Baseline Neutrino Experiments
• Decoherence, matter effect, neutrino hierarchy signature in long baseline experiments
• Dissipative Effect in Long Baseline Neutrino Experiments
• Neutrino Oscillation Probabilities in Matter with Direct and Indirect Unitarity Violation in the Lepton Mixing Matrix
• Exact and Approximate Formulas for Neutrino Mixing and Oscillations with Non-Standard Interactions
• Matter Density Profile Shape Effects at DUNE
• Constraints for non-standard interaction epsilon_{e tau}V_e from nu_e appearance in MINOS and T2K
• Physics with Reactor Neutrinos
• Next generation long baseline experiments on the path to leptonic CP violation
• Effects of nonstandard neutrino interactions at PINGU
• Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with E \lesssim 1 GeV
• Probing Neutrino Oscillation Parameters using High Power Superbeam from ESS
• Neutrino Matter Effect Invariants and the Observables of Neutrino Oscillations
• Simple and Precise Factorization of the Jarlskog Invariant for Neutrino Oscillations in Matter
• Non-standard interaction in neutrino oscillations and recent Daya Bay, T2K experiments
• On Neutrino Mixing in Matter and CP and T Violation Effects in Neutrino Oscillations
• Determining the Octant of ${\theta }_{23}$ at LBNE in conjunction with Reactor Experiments
• Magical properties of 2540 Km baseline Superbeam Experiment
• Rotations Versus Perturbative Expansions for Calculating Neutrino Oscillation Probabilities in Matter
• Understanding CP phase-dependent measurements at neutrino superbeams in terms of bi-rate graphs
• Three-flavour oscillations with accelerator neutrino beams
• 2540 km: Bimagic baseline for neutrino oscillation parameters
• Optimized Two-Baseline Beta-Beam Experiment
• Extrinsic and Intrinsic CPT Asymmetries in Neutrino Oscillations
• Neutrino hierarchy from CP-blind observables with high density magnetized detectors
• A prediction of neutrino mixing matrix with CP violating phase
• Measurement of ${\nu }_{\mu }$ and ${\bar{\nu }}_{\mu }$ Neutral Current ${\pi }^0\to \gamma \gamma$ Production in the ArgoNeuT Detector
• A CERN-based high-intensity high-energy proton source for long baseline neutrino oscillation experiments with next-generation large underground detectors for proton decay searches and neutrino physics and astrophysics
• Direct test of the MSW effect by the solar appearance term in beam experiments
• Renormalization-Group Equations of Neutrino Masses and Flavor Mixing Parameters in Matter
• Neutrino quantum decoherence engendered by neutrino radiative decay
• Leptonic commutators and clean T violation in neutrino oscillations
• Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter
• Parameter symmetries of neutrino oscillations in vacuum, matter, and approximation schemes
• A Possible Future Long Baseline Neutrino and Nucleon Decay Experiment with a 100 kton Liquid Argon TPC at Okinoshima using the J-PARC Neutrino Facility
• Neutrino mixing in matter
• Perturbing neutrino oscillations around the solar resonance
• Neutrino oscillation physics at an upgraded CNGS with large next generation liquid Argon TPC detectors
• Determination of the neutrino mass hierarchy in the regime of small matter effect
• Synergies between neutrino oscillation experiments: An `adequate' configuration for LBNO
• Time Reversal in Neutrino Oscillations
• Why Is The Neutrino Oscillation Formula Expanded In $\Delta m_{21}^2/\Delta m_{31}^2$ Still Accurate Near The Solar Resonance In Matter?
• Non-standard neutrino oscillations: perspective from unitarity triangles
• Neutrino Oscillation in Dense Matter
• Measurement of atmospheric neutrino oscillations with very large volume neutrino telescopes
• Sum rules of four-neutrino mixing in matter
• On the Properties of the Effective Jarlskog Invariant for Three-flavor Neutrino Oscillations in Matter
• Effective Neutrino Mixing and Oscillations in Dense Matter
• The need for an early anti-neutrino run of NOvA
• Looking into Analytical Approximations for Three-flavor Neutrino Oscillation Probabilities in Matter
• Large Non-perturbative Effects of Small Δm^2_{21}/Δm^2_{31} and \sin θ_{13} on Neutrino Oscillation and CP Violation in Matter
• A compact analytical approximation for a light sterile neutrino oscillation in matter
• The Kobayashi-Maskawa Parametrization of Lepton Flavor Mixing and Its Application to Neutrino Oscillations in Matter
• Measurement of three-family neutrino mixing and search for CP violation
• Sum rules and asymptotic behaviors of neutrino mixing in dense matter
• Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations
• Enhancement of CP Violating terms for Neutrino Oscillation in Earth Matter
• Do T asymmetries for neutrino oscillations in uniform matter have a CP-even component?
• Discriminating sterile neutrinos and unitarity violation with CP invariants
• Probing CP violation at LBNE with reactor experiments
• Revisiting the sensitivity studies for leptonic CP violation and mass hierarchy with T2K, NOvA and LBNE experiments
• CP violation and mass hierarchy at medium baselines in the large theta(13) era
• Proposal of a Simple Method to Estimate Neutrino Oscillation Probability and CP Violation in Matter
• Measuring Oscillations with A Million Atmospheric Neutrinos
• Neutrino amplitude decomposition in matter
• Neutrino Oscillations with the MINOS, MINOS+, T2K, and NOvA Experiments
• Connecting Leptonic Unitarity Triangle to Neutrino Oscillation with CP Violation in Vacuum and in Matter
• Leptonic CP Violation and Leptogenesis
• Understanding the degeneracies in NO$\nu$A data
• Neutrino Oscillation in Matter and Parameters $s_{13},{\delta }_{CP}$
• Physics prospects with the second oscillation maximum at Deep Underground Neutrino Experiment
• Effect of spacetime geometry on neutrino oscillations
• Symmetry Finder applied to the 1-3 mass eigenstate exchange symmetry
• On the determination of the leptonic CP phase
• Residual Symmetries Applied to Neutrino Oscillations at NO$\nu$A and T2K
• Lectures on neutrino phenomenology
• Theoretical Aspects of Neutrino Oscillation
• Measuring the Leptonic CP Phase in ${\nu }_{\mu }\to {\nu }_{\mu }$ Oscillations
• Future Precision Neutrino Oscillation Experiments and Theoretical Implications
• Towards extracting the best possible results from NOvA
• Improving CP Measurement with THEIA and Muon Decay at Rest
• Learning from tau appearance
• Tensions between the appearance data of T2K and NOvA
• Neutrino Parameters from Reactor and Accelerator Neutrino Experiments
• Rephasing invariance and the neutrino mu-tau symmetry
• Matter vs. vacuum oscillations at long baseline accelerator neutrino experiments
• Constant matter neutrino oscillations in a parametrization-free formulation
• From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes
• Physics Potential of a 2540 Km Baseline Superbeam Experiment
• Evolution of Neutrino Mass-Mixing Parameters in Matter with Non-Standard Interactions
• The Smallness of Matter Effects in Long-Baseline Muon Neutrino Disappearance
• Neutrino amplitude decomposition: Toward observing the atmospheric - solar wave interference
• Radiative corrections to the lepton flavor mixing in dense matter
• Physics of Massive Neutrinos
• Improved Theory of Neutrino Oscillations in Matter
• Estimating matter induced CPT violation in Long-Baseline Neutrino Experiments
• Analytical Theory of Neutrino Oscillations in Matter with CP violation
• Neutrino oscillations and new physics
• Comparative study of the 1-2 exchange symmetries in neutrino frameworks with global and local validities
• Review of Recent Neutrino Physics Research
• Running of Oscillation Parameters in Matter with Flavor-Diagonal Non-Standard Interactions of the Neutrino
• Neutrino Masses in a Neutrinosphere
• Revising the Solution of the Neutrino Oscillation Parameter Degeneracies at Neutrino Factories
• One-Loop Effects in the Neutrino Matter Potential and Implications for Non-Standard Interactions
• A Nearest-neighbor Expansion of Lepton Flavor Mixing in Powers of the $\mu$-$\tau$ Permutation Symmetry Breaking Effect
• Magnus Expansion and Three-Neutrino Oscillations in Matter
• Standard and Non-Standard Aspects of Neutrino Physics
• Signals of eV-scale sterile neutrino at long baseline neutrino experiments
• Matter neutrino oscillations, an approximation in a parametrization-free framework
• Long baseline neutrino oscillations: Theoretical aspects
• T versus CP effects in DUNE and T2HK
• Torsional modulation of atmospheric neutrino oscillation