Looking into Analytical Approximations for Three-flavor Neutrino Oscillation Probabilities in Matter

Abstract

Motivated by tremendous progress in neutrino oscillation experiments, we derive a new set of simple and compact formulas for three-flavor neutrino oscillation probabilities in matter of a constant density. A useful definition of the $\eta$-gauge neutrino mass-squared difference ${\Delta }_{\ast }^{}\equiv \eta {\Delta }_{31}^{}+(1-\eta ){\Delta }_{32}^{}$ is introduced, where ${\Delta }_{ji}^{}\equiv m_j^2-m_i^2$ for $ji=21,31,32$ are the ordinary neutrino mass-squared differences and $0\le \eta \le 1$ is a real and positive parameter. Expanding neutrino oscillation probabilities in terms of $\alpha \equiv {\Delta }_{21}^{}/{\Delta }_{\ast }^{}$, we demonstrate that the analytical formulas can be remarkably simplified for $\eta ={\cos }^2{\theta }_{12}^{}$, with ${\theta }_{12}^{}$ being the solar mixing angle. As a by-product, the mapping from neutrino oscillation parameters in vacuum to their counterparts in matter is obtained at the order of $\mathcal{O}({\alpha }^2)$. Finally, we show that our approximate formulas are not only valid for an arbitrary neutrino energy and any baseline length, but also still maintaining a high level of accuracy.

arXiv comment34 pages, 5 figures; v2: reference added, to appear in JHEP

References in corpus (30)

• Neutrino Physics with JUNO
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Golden measurements at a neutrino factory
• Mass and Flavor Mixing Schemes of Quarks and Leptons
• Analytic Approximations for Three Neutrino Oscillation Parameters and Probabilities in Matter
• Series expansions for three-flavor neutrino oscillation probabilities in matter
• Neutrino masses and mixings: Status of known and unknown $3\nu$ parameters
• Diffractive-Like (or Parametric-Resonance-Like?) Enhancement of the Earth (Day-Night) Effect for Solar Neutrinos Crossing the Earth Core
• Global Analyses of Neutrino Oscillation Experiments
• A Very Intense Neutrino Super Beam Experiment for Leptonic CP Violation Discovery based on the European Spallation Source Linac: A Snowmass 2013 White Paper
• Three flavor neutrino oscillations in matter
• Neutrino Mass Spectrum with ${\nu }_{\mu }$ $\to$ ${\nu }_s$ Oscillations of Atmospheric Neutrinos
• New Conditions for a Total Neutrino Conversion in a Medium
• Leptonic Unitarity Triangle and CP-violation
• CP and T Violation in Neutrino Oscillations and Invariance of Jarlskog's Determinant to Matter Effects
• Parametric Resonance in Oscillations of Atmospheric Neutrinos?
• Compact Perturbative Expressions For Neutrino Oscillations in Matter
• Unitarity triangles and geometrical description of CP violation with Majorana neutrinos
• Enhancing Mechanisms of Neutrino Transitions in a Medium of Nonperiodic Constant - Density Layers and in the Earth
• New Formulation of Matter Effects on Neutrino Mixing and CP Violation
• Neutrino Oscillation and CP Violation
• MOMENT: a muon-decay medium-baseline neutrino beam facility
• Simple and Compact Expressions for Neutrino Oscillation Probabilities in Matter
• Analytical Approximation of the Neutrino Oscillation Matter Effects at large ${\theta }_{13}$
• Leptonic Unitarity Triangles in Matter
• Reconstruction of the Neutrino Mixing Matrix and Leptonic Unitarity Triangles from Long-baseline Neutrino Oscillations
• Sum Rules of Neutrino Masses and CP Violation in the Four-Neutrino Mixing Scheme
• Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with E \lesssim 1 GeV
• The MOMENT to search for CP violation
• Leptonic Unitarity Triangles and Effective Mass Triangles of the Majorana Neutrinos

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